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BEGIN:VEVENT
SUMMARY:Wojciech Niemiro (University of Warsaw)
DTSTART:20200515T081500Z
DTEND:20200515T093000Z
DTSTAMP:20260404T110823Z
UID:MarkovProcessesWroclaw/1
DESCRIPTION:Title: Estimation of the growth rate for Lévy processes wi
th bounded positive jumps\nby Wojciech Niemiro (University of Warsaw)
as part of Theory of Markov Semigroups and Schrödinger Operators\n\nAbstr
act: TBA\n
LOCATION:https://stable.researchseminars.org/talk/MarkovProcessesWroclaw/1
/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Toshihiro Uemura (Kansai University)
DTSTART:20200522T081500Z
DTEND:20200522T093000Z
DTSTAMP:20260404T110823Z
UID:MarkovProcessesWroclaw/2
DESCRIPTION:Title: On symmetric stable-type processes with singular/deg
enerate coefficitents\nby Toshihiro Uemura (Kansai University) as part
of Theory of Markov Semigroups and Schrödinger Operators\n\nAbstract: TB
A\n
LOCATION:https://stable.researchseminars.org/talk/MarkovProcessesWroclaw/2
/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Mateusz Kwaśnicki (Wrocław University of Science and Technology)
DTSTART:20200529T081500Z
DTEND:20200529T091500Z
DTSTAMP:20260404T110823Z
UID:MarkovProcessesWroclaw/3
DESCRIPTION:Title: Spectral theory for non-symmetric Lévy processes in
the half-line\nby Mateusz Kwaśnicki (Wrocław University of Science
and Technology) as part of Theory of Markov Semigroups and Schrödinger Op
erators\n\nAbstract: TBA\n
LOCATION:https://stable.researchseminars.org/talk/MarkovProcessesWroclaw/3
/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Jan Swart (Czech Academy of Sciences)
DTSTART:20201009T081500Z
DTEND:20201009T091500Z
DTSTAMP:20260404T110823Z
UID:MarkovProcessesWroclaw/4
DESCRIPTION:Title: Recursive tree processes and the mean-field limit of
stochastic flows\nby Jan Swart (Czech Academy of Sciences) as part of
Theory of Markov Semigroups and Schrödinger Operators\n\n\nAbstract\nInt
eracting particle systems can often be constructed from a graphical repres
entation\, by applying local maps at the times of associated Poisson proce
sses. This leads to a natural coupling of systems started in different ini
tial states. In the talk\, we will look at interacting particle systems on
the complete graph in the mean-field limit\, i.e.\, as the number of vert
ices tends to infinity. We will not only be interested in the mean-field l
imit of a single process\, but mainly in how several coupled processes beh
ave in the limit. In particular\, we want to know how sensitive the Poisso
n construction is to small changes in the initial state. This turns out to
be closely related to recursive tree processes as studied by Aldous and B
andyopadyay\, which are a sort of Markov chains in which time has a tree-l
ike structure and in which the state of each vertex is a random function o
f its descendants. The abstract theory will be demonstrated on an example
of a particle system with cooperative branching and deaths.\n\nThis is joi
nt work with Anja Sturm and Tibor Mach.\n
LOCATION:https://stable.researchseminars.org/talk/MarkovProcessesWroclaw/4
/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Zbigniew J. Jurek (University of Wroclaw)
DTSTART:20201016T081500Z
DTEND:20201016T091500Z
DTSTAMP:20260404T110823Z
UID:MarkovProcessesWroclaw/5
DESCRIPTION:Title: Compositions of some random integral mappings (and a
conjecture)\nby Zbigniew J. Jurek (University of Wroclaw) as part of
Theory of Markov Semigroups and Schrödinger Operators\n\n\nAbstract\nIn t
he 1980s\, Lévy class L of selfdecomposable distributions was characteriz
ed as distributions of some homomorphisms between convolution subsemigroup
s of ID (the semigroup of all infinitely divisible measures). We will show
that compositions of those random integrals (mappings) can be always expr
essed as another single random integral mapping. That fact is illustrated
by some old Thorin class T. Finally\, we will discuss a conjecture that (s
ome) classes of limit laws always admit random integral representations.\n
LOCATION:https://stable.researchseminars.org/talk/MarkovProcessesWroclaw/5
/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Nicolas Perkowski (Free University of Berlin)
DTSTART:20201023T081500Z
DTEND:20201023T091500Z
DTSTAMP:20260404T110823Z
UID:MarkovProcessesWroclaw/6
DESCRIPTION:Title: Mass asymptotics for the 2d parabolic Anderson model
with white noise potential\nby Nicolas Perkowski (Free University of
Berlin) as part of Theory of Markov Semigroups and Schrödinger Operators\
n\n\nAbstract\nWe study the long time behavior of the total mass of the 2d
parabolic Anderson model (PAM) with white noise potential\, which is the
universal scaling limit of 2d branching random walks in small random envir
onments. There are several known results on the long time behavior of the
PAM for more regular potentials\, but the 2d white noise is very singular
and it requires renormalization techniques. In particular\, the Feynman–
Kac representation\, usually the main tool for deriving asymptotics\, brea
ks down. To overcome this problem we use a measure transform and we introd
uce a new “partial Feynman–Kac representation”. The new representati
on is based on a diffusion with distributional drift\, and we derive Gauss
ian heat kernel bounds for such diffusions. \n\nBased on joint works with
Wolfgang König and Willem van Zuijlen.\n
LOCATION:https://stable.researchseminars.org/talk/MarkovProcessesWroclaw/6
/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Workshop (TU Dresden & Wroclaw University of Technology)
DTSTART:20201026T140000Z
DTEND:20201026T164500Z
DTSTAMP:20260404T110823Z
UID:MarkovProcessesWroclaw/7
DESCRIPTION:Title: Nonlocal Operators and Markov Processes\, Oct 26–3
0\, 2020\nby Workshop (TU Dresden & Wroclaw University of Technology)
as part of Theory of Markov Semigroups and Schrödinger Operators\n\n\nAbs
tract\nFormat: open Zoom webinar\n\nRegistration and details: http://prac.
im.pwr.wroc.pl/~bogdan/nomp.html\n\nSchedule (all times given in Wroclaw D
resden time=GMT+2h):\n\n\nMonday\, 26 Oct:\n\n15:00-15:45 and 16:00-16:45
Xavier Ros-Oton\, Boundary regularity for nonlocal operators 1\n\n17:00-17
:45 Franziska Kühne\, Lévy-type processes 1\n\n\nTuesday\, 27 Oct:\n\n15
:00-15:45 and 16:00-16:45 Xavier Ros-Oton\, Boundary regularity for nonloc
al operators 2\n\n17:00-17:45 Franziska Kühne\, Lévy-type processes 2\n\
nWednesday\, 28 Oct:\n\n\n15:00-15:45 and 16:00-16:45 Xavier Ros-Oton\, Bo
undary regularity for nonlocal operators 3\n\n17:00-17:45 Mateusz Kwaśnic
ki\, Potential theory of Markov processes 1\n\nThursday\, 29 Oct:\n\n\n15:
00-15:45 and 16:00-16:45 Xavier Ros-Oton\, Boundary regularity for nonloca
l operators 4\n\n17:00-17:45 Mateusz Kwaśnicki\, Potential theory of Mark
ov processes 2\n\n\nFriday\, 30 Oct (note different hour):\n\nRecent Topic
s and Developments:\n\n10:15-11:00 Enrico Valdinoci\, The Bernstein techni
que for integrodifferential equations\n\n11:15-12:00 Bartłomiej Dyda\, On
fractional Hardy inequalities\n\n12:15-13:00 Alex Kulik\, Parametrix tech
nique for complicated Lévy-type models\n
LOCATION:https://stable.researchseminars.org/talk/MarkovProcessesWroclaw/7
/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Krzysztof Burdzy (University of Washington)
DTSTART:20201112T171500Z
DTEND:20201112T181500Z
DTSTAMP:20260404T110823Z
UID:MarkovProcessesWroclaw/8
DESCRIPTION:Title: Fleming–Viot processes and $X=AX+B$ equation\n
by Krzysztof Burdzy (University of Washington) as part of Theory of Markov
Semigroups and Schrödinger Operators\n\n\nAbstract\nI will start with a
review of Fleming–Viot processes. I will state two open problems and som
e partial results. A specific Fleming–Viot model was an inspiration for
a Law of Iterated Logarithm-type result. This result has a rather limited
significance. The method of proof\, we hope\, may have an independent inte
rest.\n\n\nJoint work with Bartosz Kołodziejek and Tvrtko Tadić.\n
LOCATION:https://stable.researchseminars.org/talk/MarkovProcessesWroclaw/8
/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Yehuda Pinchover (Technion – Israel Institute of Technology)
DTSTART:20201211T091500Z
DTEND:20201211T101500Z
DTSTAMP:20260404T110823Z
UID:MarkovProcessesWroclaw/9
DESCRIPTION:Title: On families of optimal Hardy-weights for linear seco
nd-order elliptic operators\nby Yehuda Pinchover (Technion – Israel
Institute of Technology) as part of Theory of Markov Semigroups and Schrö
dinger Operators\n\n\nAbstract\nWe construct families of optimal Hardy-wei
ghts for a subcritical linear second-order elliptic operator using a one-d
imensional reduction. More precisely\, we first characterize all optimal H
ardy-weights with respect to one-dimensional subcritical Sturm-Liouville o
perators on $(a\,b)$\, $\\infty \\leq a < b \\leq \\infty$\, and then appl
y this result to obtain families of optimal Hardy inequalities for general
linear second-order elliptic operators in higher dimensions. This is a jo
int work with Idan Versano.\n
LOCATION:https://stable.researchseminars.org/talk/MarkovProcessesWroclaw/9
/
END:VEVENT
BEGIN:VEVENT
SUMMARY:René Schilling (Technische Universität Dresden)
DTSTART:20210115T091500Z
DTEND:20210115T101500Z
DTSTAMP:20260404T110823Z
UID:MarkovProcessesWroclaw/10
DESCRIPTION:Title: Some Remarks on the Liouville Theorem for Generator
s of Lévy Processes\nby René Schilling (Technische Universität Dres
den) as part of Theory of Markov Semigroups and Schrödinger Operators\n\n
\nAbstract\nWe discuss various proofs of the (strong) Liouville property f
or non-local operators.\n
LOCATION:https://stable.researchseminars.org/talk/MarkovProcessesWroclaw/1
0/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Stefan Geiss (University of Jyväskylä)
DTSTART:20201120T091500Z
DTEND:20201120T101500Z
DTSTAMP:20260404T110823Z
UID:MarkovProcessesWroclaw/11
DESCRIPTION:Title: On Riemann–Liouville operators\, BMO\, and gradie
nt estimates in the Lévy–Itô space\nby Stefan Geiss (University of
Jyväskylä) as part of Theory of Markov Semigroups and Schrödinger Oper
ators\n\n\nAbstract\nWe discuss in a stochastic framework the interplay be
tween Riemann–Liouville operators applied to càdlàg processes\, real i
nterpolation\, bounded mean oscillation\, and estimates for gradient proce
sses on the Lévy–Itô space. We prove upper and lower bounds for these
gradient processes\, where we are concerned with Hilbert space valued grad
ients and where its regularity depends on the direction within the Hilbert
space. It turns out that certain Hölder properties of the terminal funct
ions transfer into a singularity in time that can be compensated by Rieman
n–Liouville operators.\n\nThe talk is based on the preprint:\n\n S. G
eiss\, T.T. Nguyen: On Riemann–Liouville operators\, BMO\, gradient esti
mates in the Lévy–Itô space\, and approximation\, arXiv:2009.00899.\n
LOCATION:https://stable.researchseminars.org/talk/MarkovProcessesWroclaw/1
1/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Alain-Sol Sznitman (ETH Zürich)
DTSTART:20210319T091500Z
DTEND:20210319T101500Z
DTSTAMP:20260404T110823Z
UID:MarkovProcessesWroclaw/12
DESCRIPTION:Title: Excess deviations for points disconnected by random
interlacements\nby Alain-Sol Sznitman (ETH Zürich) as part of Theory
of Markov Semigroups and Schrödinger Operators\n\n\nAbstract\nThe study
of large deviation events involving disconnection by random interlacements
or of similar large deviation events for the closely related model of lev
el-set percolation of the Gaussian free field has been an active subject o
f research in the last years.\nIn this talk we describe a recent result co
ncerning random interlacements on Z^d\, d≥3\, in the strongly percolativ
e regime. Given a large box centered at the origin we investigate the expo
nential rate of decay of the probability that the box contains an excessiv
e fraction of points that are disconnected by random interlacements from t
he boundary of a box of double size.\n
LOCATION:https://stable.researchseminars.org/talk/MarkovProcessesWroclaw/1
2/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Dariusz Buraczewski (University of Wrocław)
DTSTART:20201127T091500Z
DTEND:20201127T101500Z
DTSTAMP:20260404T110823Z
UID:MarkovProcessesWroclaw/13
DESCRIPTION:Title: On the branching random walk and the derivative mar
tingale\nby Dariusz Buraczewski (University of Wrocław) as part of Th
eory of Markov Semigroups and Schrödinger Operators\n\n\nAbstract\nWe wil
l describe the branching random walk (BRW) and its fundamental properties
including the central limit theorem. A crucial role in analyzing the BRW i
s played by the so-called derivative martingale. We will discuss new resul
ts concerning the derivative martingale. The talk is based on a joint work
with Aleksander Iksanov and Bastien Mallein.\n
LOCATION:https://stable.researchseminars.org/talk/MarkovProcessesWroclaw/1
3/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Martin Hairer (Imperial College London)
DTSTART:20201218T091500Z
DTEND:20201218T101500Z
DTSTAMP:20260404T110823Z
UID:MarkovProcessesWroclaw/14
DESCRIPTION:Title: Averaging of non-Markovian SDEs\nby Martin Hair
er (Imperial College London) as part of Theory of Markov Semigroups and Sc
hrödinger Operators\n\n\nAbstract\nWe consider slow / fast systems where
the slow system is driven by fractional Brownian motion with Hurst paramet
er $H > 1/2$. We show that unlike in the case $H=1/2$\, convergence to the
averaged solution takes place in probability and the limiting process sol
ves the “naively” averaged equation. Our proof strongly relies on the
recently obtained stochastic sewing lemma.\n\nJoint with Xue-Mei Li.\n
LOCATION:https://stable.researchseminars.org/talk/MarkovProcessesWroclaw/1
4/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Damir Kinzebulatov (Laval University)
DTSTART:20201204T110000Z
DTEND:20201204T120000Z
DTSTAMP:20260404T110823Z
UID:MarkovProcessesWroclaw/15
DESCRIPTION:Title: Fractional Kolmogorov operator and desingularizing
weights\nby Damir Kinzebulatov (Laval University) as part of Theory of
Markov Semigroups and Schrödinger Operators\n\n\nAbstract\nWe establish
sharp two-sided bounds on the heat kernel of the fractional Laplacian pert
urbed by Hardy-type drift by transferring it to an appropriate weighted sp
ace with singular weight. The talk is based on joint papers with Yu.A.Seme
nov and K.Szczypkowski.\n
LOCATION:https://stable.researchseminars.org/talk/MarkovProcessesWroclaw/1
5/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Karol Szczypkowski (Wrocław University of Science and Technology)
DTSTART:20201106T091500Z
DTEND:20201106T101500Z
DTSTAMP:20260404T110823Z
UID:MarkovProcessesWroclaw/16
DESCRIPTION:Title: Non-symmetric Lévy processes\nby Karol Szczypk
owski (Wrocław University of Science and Technology) as part of Theory of
Markov Semigroups and Schrödinger Operators\n\nAbstract: TBA\n
LOCATION:https://stable.researchseminars.org/talk/MarkovProcessesWroclaw/1
6/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Lorenzo Toniazzi (University of Otago)
DTSTART:20210129T091500Z
DTEND:20210129T101500Z
DTSTAMP:20260404T110823Z
UID:MarkovProcessesWroclaw/18
DESCRIPTION:Title: Censored stable subordinators and relaxation\nb
y Lorenzo Toniazzi (University of Otago) as part of Theory of Markov Semig
roups and Schrödinger Operators\n\n\nAbstract\nMotivated by popular model
s of non-exponential relaxation based on stable subordinators\, we conside
r a stable subordinator censored when jumping above a barrier. We show thi
s process hits the barrier in a finite time\, whose Laplace transform solv
es the ‘censored’ relaxation equation. This solution turns out to be a
completely monotone series\, modeling algebraic decay of order between 1
and 2\; decay unattainable by comparable models. We also discuss how we id
entified a new sub-diffusion process and several unanswered questions.\n\n
Joint work with Qiang Du and Zirui Xu (arXiv:1906.07296).\n
LOCATION:https://stable.researchseminars.org/talk/MarkovProcessesWroclaw/1
8/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Radosław Adamczak (University of Warsaw)
DTSTART:20210122T091500Z
DTEND:20210122T101500Z
DTSTAMP:20260404T110823Z
UID:MarkovProcessesWroclaw/19
DESCRIPTION:Title: Modified log-Sobolev inequalities\, Beckner inequal
ities and moment estimates\nby Radosław Adamczak (University of Warsa
w) as part of Theory of Markov Semigroups and Schrödinger Operators\n\n\n
Abstract\nI will present recent results concerning the equivalence between
the modified log-Sobolev inequality and a family of Beckner type inequali
ties with constants uniformly separated from zero. Next I will discuss mom
ent estimates which can be derived from such inequalities\, generalizing p
revious results due to Aida and Stroock\, based on a stronger log-Sobolev
inequality due to Federbush and Gross. If time permits I will present exam
ples to moment estimates for certain Cauchy type measures\, for invariant
measures of Glauber dynamics and on the Poisson path space.\n\nBased on jo
int work with B. Polaczyk and M. Strzelecki.\n
LOCATION:https://stable.researchseminars.org/talk/MarkovProcessesWroclaw/1
9/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Daesung Kim (Uniwersytet Illinois at Urbana-Champaign)
DTSTART:20210305T130000Z
DTEND:20210305T140000Z
DTSTAMP:20260404T110823Z
UID:MarkovProcessesWroclaw/20
DESCRIPTION:Title: Hardy–Stein identity and Fourier multipliers\
nby Daesung Kim (Uniwersytet Illinois at Urbana-Champaign) as part of Theo
ry of Markov Semigroups and Schrödinger Operators\n\n\nAbstract\nThe clas
sical Hardy-Stein identity gives a representation of the $L^p$ norm of a f
unction in terms of a semigroup associated with Brownian motion. The ident
ity was used to derive the $L^p$ boundedness of the Littlewood-Paley squar
e functions\, which leads to that of Fourier multiplier operators. In this
talk\, we discuss the extension of the Hardy-Stein identity to non-symmet
ric pure jump Levy processes and a certain class of martingales. The proof
is based on the Ito's formula for a general stochastic process.\n
LOCATION:https://stable.researchseminars.org/talk/MarkovProcessesWroclaw/2
0/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Zbigniew Palmowski (Wrocław University of Science and Technology)
DTSTART:20210312T091500Z
DTEND:20210312T101500Z
DTSTAMP:20260404T110823Z
UID:MarkovProcessesWroclaw/21
DESCRIPTION:Title: On the renewal theorem for maxima on trees\nby
Zbigniew Palmowski (Wrocław University of Science and Technology) as part
of Theory of Markov Semigroups and Schrödinger Operators\n\n\nAbstract\n
We consider the distributional fixed-point equation: \\[R \\stackrel{\\mat
hcal{D}}{=} Q \\vee \\left( \\bigvee_{i=1}^N C_i R_i \\right)\,\\] where t
he $R_i$ are i.i.d. copies of $R$\, independent of the vector $(Q\, N\, \\
{C_i\\})$\, with $N \\in \\mathbb{N}$\, $Q\, C_i \\geq 0$ and $P(Q > 0) >
0$. By setting $W = \\log R$\, $X_i = \\log C_i$\, $Y = \\log Q$ it is equ
ivalent to the high-order Lindley equation \\[W \\stackrel{\\mathcal{D}}{=
} \\max\\left\\{ Y\, \\\, \\max_{1 \\leq i \\leq N}(X_i + W_i) \\right\\}.
\\] It is known that under Kesten assumptions\,\\[P(W > t) \\sim H e^{-\\a
lpha t}\, \\qquad t \\to \\infty\,\\]where $\\alpha>0$ solves the Cramér-
-Lundberg equation $E \\left[ \\sum_{j=1}^N C_i^\\alpha \\right] = E\\left
[ \\sum_{i=1}^N e^{\\alpha X_i} \\right] = 1$. The main goal of this paper
is to provide an explicit representation for $P(W > t)$\, which can be di
rectly connected to the underlying weighted branching process where $W$ is
constructed and that can be used to construct unbiased and strongly effic
ient estimators for all $t$. Furthermore\, we show how this new representa
tion can be directly analyzed using Alsmeyer's Markov renewal theorem\, yi
elding an alternative representation for the constant $H$. We provide nume
rical examples illustrating the use of this new algorithm.\n\nThis is a jo
int work with Bojan Basrak\, Michael Conroy and Mariana Olvera-Cravioto (a
rXiv:2004.08966).\n
LOCATION:https://stable.researchseminars.org/talk/MarkovProcessesWroclaw/2
1/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Workshop (TU Dresden & Wrocław University of Science and Technolo
gy)
DTSTART:20210322T090000Z
DTEND:20210322T140000Z
DTSTAMP:20260404T110823Z
UID:MarkovProcessesWroclaw/22
DESCRIPTION:Title: Nonlocal Operators and Markov Processes II workshop
\, Mar 22–26\, 2021\nby Workshop (TU Dresden & Wrocław University o
f Science and Technology) as part of Theory of Markov Semigroups and Schr
ödinger Operators\n\n\nAbstract\nFormat: Virtual Zoom Conference\n\nRegis
tration and details: http://prac.im.pwr.wroc.pl/~bogdan/nomp-II.html\n\nSc
hedule:\n\n(times are given in Wroclaw-Dresden time -- GMT+1h)\n\n\nMonday
\, 22 Mar:\n\n10:00-11:00 Alex Kulik\n\n11:00-12:00 Reinhard Höpfner\n\n1
4:00-15:00 René Schilling\n\n\nTuesday\, 23 Mar:\n\n10:00-11:00 Reinhard
Höpfner\n\n11:00-12:00 Alex Kulik\n\n14:00-15:00 Noufel Frikha\n\n\nWedne
sday\, 24 Mar:\n\n10:00-11:00 Arturo Kohatsu-Higa\n\n11:00-12:00 Arnaud Gl
oter\n\n14:00-15:00 Reinhard Höpfner\n\n\n\nThursday\, 25 Mar:\n\n10:00-1
1:00 Andrea Pascucci\n\n11:00-12:00 Arturo Kohatsu-Higa\n\n14:00-15:00 Arn
aud Gloter \n\n\n\nFriday\, 26 Mar:\n\n10:00-11:00 Arnaud Gloter\n\n11:00-
12:00 Alex Kulik\n\n14:00-15:00 Arturo Kohatsu-Higa\n
LOCATION:https://stable.researchseminars.org/talk/MarkovProcessesWroclaw/2
2/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Zbigniew Palmowski (Wrocław University of Science and Technology)
DTSTART:20210423T081500Z
DTEND:20210423T091500Z
DTSTAMP:20260404T110823Z
UID:MarkovProcessesWroclaw/23
DESCRIPTION:Title: Extreme positions of regularly varying branching ra
ndom walk in random environment\nby Zbigniew Palmowski (Wrocław Unive
rsity of Science and Technology) as part of Theory of Markov Semigroups an
d Schrödinger Operators\n\n\nAbstract\nIn this talk\, we consider a Branc
hing Random Walk (BRW) on the real line where the underlying genealogical
structure is given through a supercritical branching process in i.i.d. env
ironment and satisfies Kesten–Stigum condition. The displacements coming
from the same parent are assumed to have jointly regularly varying tails.
Conditioned on the survival of the underlying genealogical tree\, we prov
e that the appropriately normalized (depends on the expected size of the n
th generation given the environment) maximum among positions at the nth ge
neration converges weakly to a scale-mixture of Frechét random variable.
Furthermore\, we derive the weak limit of the extremal processes composed
of appropriately scaled positions at the nth generation and show that the
limit point process is a member of the randomly scaled scale-decorated Poi
sson point processes (SScDPPP). Hence\, an analog of the predictions by Br
unet and Derrida (2011) holds.\n\nThis is a joint work with Ayan Bhattacha
rya (arXiv:2101.05369).\n
LOCATION:https://stable.researchseminars.org/talk/MarkovProcessesWroclaw/2
3/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Julia Lenczewska (Wrocław University of Science and Technology)
DTSTART:20210409T081500Z
DTEND:20210409T091500Z
DTSTAMP:20260404T110823Z
UID:MarkovProcessesWroclaw/24
DESCRIPTION:Title: Optimal Hardy inequality for the fractional Laplaci
an on L^p\nby Julia Lenczewska (Wrocław University of Science and Tec
hnology) as part of Theory of Markov Semigroups and Schrödinger Operators
\n\n\nAbstract\nWe give an optimal Hardy inequality for a generalization o
f the quadratic form\, the Sobolev–Bregman form\, of the fractional Lapl
acian on $L^p(\\mathbb R^d)$. We present an application of our results to
the contractivity of the Feynman–Kac semigroup $\\tilde P_t$\ngenerated
by $\\Delta^{\\alpha/2}+\\kappa |x|^{-\\alpha}$. The talk is based on a jo
int work with Krzysztof Bogdan\, Tomasz Jakubowski and Katarzyna Pietruska
-Pałuba\, available at arXiv:2103.06550.\n
LOCATION:https://stable.researchseminars.org/talk/MarkovProcessesWroclaw/2
4/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Longmin Wang (Nankai University)
DTSTART:20210416T081500Z
DTEND:20210416T091500Z
DTSTAMP:20260404T110823Z
UID:MarkovProcessesWroclaw/25
DESCRIPTION:Title: Isotropic alpha-self-similar Markov process with a
skew-product structure\nby Longmin Wang (Nankai University) as part of
Theory of Markov Semigroups and Schrödinger Operators\n\n\nAbstract\nLet
$\\tau_C$\nbe the exit time from a cone $C$ of an isotropic $\\alpha$-sel
f-similar Markov process $X_t$\nwith a skew-product structure\, that is $X
_t$\nis a product of its radial process and independent time changed angul
ar component $\\Theta_t$\n. Under some additional regularity assumptions\,
we prove that\n$$\n\\mathbb P_x(\\tau_C >t) \\approx h(x) t^{-\\kappa_1}\
n$$\nas $t \\to \\infty$ for $h$ and $\\kappa_1$\nidentified explicitly. T
his is a joint work with Zbigniew Palmowski.\n
LOCATION:https://stable.researchseminars.org/talk/MarkovProcessesWroclaw/2
5/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Andrea Pascucci (Alma Mater Studiorum – Università di Bologna)
DTSTART:20210430T081500Z
DTEND:20210430T091500Z
DTSTAMP:20260404T110823Z
UID:MarkovProcessesWroclaw/26
DESCRIPTION:Title: On stochastic Langevin and Fokker-Planck equations<
/a>\nby Andrea Pascucci (Alma Mater Studiorum – Università di Bologna)
as part of Theory of Markov Semigroups and Schrödinger Operators\n\n\nAbs
tract\nWe study existence\, regularity in Hölder classes and estimates fr
om above and below of the fundamental solution of a degenerate (S)PDE sati
sfying the weak Hörmander condition. We discuss different notions of intr
insic regularity. We apply a Wentzell’s formula to reduce the SPDE to a
PDE with random coefficients to which we apply the parametrix technique an
d construct a fundamental solution.\n
LOCATION:https://stable.researchseminars.org/talk/MarkovProcessesWroclaw/2
6/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Jacek Małecki (Wrocław University of Science and Technology)
DTSTART:20210514T081500Z
DTEND:20210514T091500Z
DTSTAMP:20260404T110823Z
UID:MarkovProcessesWroclaw/27
DESCRIPTION:Title: Archimedes principle for ideal gas\nby Jacek Ma
łecki (Wrocław University of Science and Technology) as part of Theory o
f Markov Semigroups and Schrödinger Operators\n\n\nAbstract\nWe prove Arc
himedes’ principle for a macroscopic ball in ideal gas consisting of poi
nt particles with non-zero mass. The main result is an asymptotic theorem\
, as the number of point particles goes to infinity and their total mass r
emains constant. We also show that\, asymptotically\, the gas has an expon
ential density as a function of height. We find the asymptotic inverse tem
perature of the gas. We derive an accurate estimate of the volume of the p
hase space using the local central limit theorem. The talk is based on a j
oint work with Krzysztof Burdzy.\n
LOCATION:https://stable.researchseminars.org/talk/MarkovProcessesWroclaw/2
7/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Tomasz Komorowski (Institute of Mathematics of the Polish Academy
of Sciences)
DTSTART:20210618T081500Z
DTEND:20210618T091500Z
DTSTAMP:20260404T110823Z
UID:MarkovProcessesWroclaw/28
DESCRIPTION:Title: Diffusive and superdiffusive limits for a kinetic e
quation with a boundary condition\nby Tomasz Komorowski (Institute of
Mathematics of the Polish Academy of Sciences) as part of Theory of Markov
Semigroups and Schrödinger Operators\n\n\nAbstract\nWe consider the limi
t of a linear kinetic equation\, with reflection-transmission-absorption a
t a point interface. The scattering kernel is degenerate. The equation ari
ses from a microscopic chain of oscillators in contact with a heat bath. I
n the absence of the interface\, the solutions exhibit either diffusive\,
or superdiffusive behavior in the long time limit\, depending on whether t
he dispersion relation for the chain is optical\, or acoustic. The latter
corresponds to either the presence\, or absence of an external potential a
cting on the chain. With the interface\, the long time limit is either the
unique solution of a heat equation with a Dirichlet boundary condition (i
n the optical case)\, or a version of the fractional in space heat equatio
n\, with reflection-transmission-absorption at the interface (in the acous
tic case). In the latter case the limit problem corresponds to a certain s
table process that is either absorbed\, reflected\, or transmitted upon cr
ossing the interface. The results have been obtained in collaboration with
G. Basile (Univ. Roma I)\, S. Olla (Univ. Paris-Dauphine)\, L. Ryzhik (St
anford Univ.) and H. Spohn (TU München).\n
LOCATION:https://stable.researchseminars.org/talk/MarkovProcessesWroclaw/2
8/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Conference
DTSTART:20210524T081500Z
DTEND:20210524T091500Z
DTSTAMP:20260404T110823Z
UID:MarkovProcessesWroclaw/29
DESCRIPTION:Title: Probability and Analysis 2021 online conference\, M
ay 24–28\, 2021\nby Conference as part of Theory of Markov Semigroup
s and Schrödinger Operators\n\n\nAbstract\nFormat: online conference (ope
n Zoom webinar -- registration required)\n\nRegistration and program: http
://pa2021.im.pwr.edu.pl/\n\nPlease note that all times in the schedule are
given in Wroclaw (Poland) time=GMT+2h.\n
LOCATION:https://stable.researchseminars.org/talk/MarkovProcessesWroclaw/2
9/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Łukasz Leżaj (Wrocław University of Science and Technology)
DTSTART:20210611T081500Z
DTEND:20210611T091500Z
DTSTAMP:20260404T110823Z
UID:MarkovProcessesWroclaw/30
DESCRIPTION:Title: Transition densities of spectrally positive Lévy p
rocesses\nby Łukasz Leżaj (Wrocław University of Science and Techno
logy) as part of Theory of Markov Semigroups and Schrödinger Operators\n\
n\nAbstract\nWe prove asymptotic behaviour of transition densities for a l
arge class of spectrally one-sided Lévy processes of unbounded variation
satisfying mild condition imposed on the second derivative of the Laplace
exponent\, or equivalently\, on the real part of the characteristic expone
nt. We also provide sharp two-sided estimates on the density when restrict
ed additionally to processes without Gaussian component.\n
LOCATION:https://stable.researchseminars.org/talk/MarkovProcessesWroclaw/3
0/
END:VEVENT
END:VCALENDAR