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BEGIN:VEVENT
SUMMARY:Richard Kenyon (Yale University)
DTSTART:20210920T150000Z
DTEND:20210920T154500Z
DTSTAMP:20260404T041857Z
UID:BIRS-21w5511/1
DESCRIPTION:Title: Multinomial models\nby Richard Kenyon (Yale University) as
part of BIRS workshop: Permutations and Probability\n\n\nAbstract\nRandom
tiling models and other stat mech models like the Potts model\non a graph
G become tractable in a certain limit of “blow up”s G_N\,\nwhere each
vertex of G is replaced with N vertices and each edge with K_{N\,N}.\nWe
give exact enumerations\, free energy\, phase transitions\, conformal inva
riance\nproperties for these models. This is joint work with Cosmin Pohoat
a.\n
LOCATION:https://stable.researchseminars.org/talk/BIRS-21w5511/1/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Arvind Ayyer (Indian Institute of Science)
DTSTART:20210920T161500Z
DTEND:20210920T170000Z
DTSTAMP:20260404T041857Z
UID:BIRS-21w5511/2
DESCRIPTION:Title: Toppleable permutations\, acyclic orientations and excedances<
/a>\nby Arvind Ayyer (Indian Institute of Science) as part of BIRS worksho
p: Permutations and Probability\n\n\nAbstract\nThe representation theory o
f the symmetric group provides several\nbeautiful combinatorial formulas.
The idea to use it to study random\nwalks comes from Diaconis and Shahshah
ani\, who used some formulas to\nbound the eigenvalues of the random trans
position shuffle\, leading to a\ncutoff phenomenon.\nOur main goal will be
to explain how to improve their L^2 bound method\nto obtain cutoff profil
es\, and more concretely how this applies to\nrandom transpositions.\n\nWe
will first recall some definitions and explain the link between\nrepresen
tation theory and Fourier analysis. Then\, we will explain the\nlimit prof
ile method\, and its generalisation to reversible Markov chains\n(by Nesto
ridi and Olesker-Taylor). Finally\, we will discuss the\nMurnagham-Nakayam
a formula and its link with the fixed points of\npermutations.\n\nThe talk
will not assume prior knowledge of representation theory\, all\nrepresent
ation theoretic statements be also explained in terms of\neigenvalues and
eigenvectors of the transition matrix.\n
LOCATION:https://stable.researchseminars.org/talk/BIRS-21w5511/2/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Louigi Addario-Berry (McGill University)
DTSTART:20210920T170000Z
DTEND:20210920T174500Z
DTSTAMP:20260404T041857Z
UID:BIRS-21w5511/3
DESCRIPTION:Title: Height bounds for random trees\nby Louigi Addario-Berry (M
cGill University) as part of BIRS workshop: Permutations and Probability\n
\n\nAbstract\nI will present new\, non-asymptotic bounds on the heights of
random combinatorial trees and conditioned Bienaymé trees\, as well as s
tochastic inequalities relating the heights of combinatorial trees with di
fferent degree sequences. The tool for all the proofs is a new approach to
coding rooted trees by sequences.\n
LOCATION:https://stable.researchseminars.org/talk/BIRS-21w5511/3/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Charles Bordenave (Institut de Mathématiques de Marseille)
DTSTART:20210921T151500Z
DTEND:20210921T154500Z
DTSTAMP:20260404T041857Z
UID:BIRS-21w5511/4
DESCRIPTION:by Charles Bordenave (Institut de Mathématiques de Marseille)
as part of BIRS workshop: Permutations and Probability\n\nAbstract: TBA\n
LOCATION:https://stable.researchseminars.org/talk/BIRS-21w5511/4/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Svante Linusson (KTH-Royal Institute of Technology Stockholm)
DTSTART:20210921T161500Z
DTEND:20210921T170000Z
DTSTAMP:20260404T041857Z
UID:BIRS-21w5511/5
DESCRIPTION:Title: Random walks in affine Weyl groups and TASEPs on signed permut
ations\nby Svante Linusson (KTH-Royal Institute of Technology Stockhol
m) as part of BIRS workshop: Permutations and Probability\n\n\nAbstract\nW
e study random reduced walks in affine Weyl groups of types B\, C and D. T
hese walks almost surely approaches one of finitely many directions each c
orresponding to a signed permutation. We compute the exact directions for
a natural set of parameters called Kac labels as weights for the walk. Thi
s settles a question by Thomas Lam\, for types B and C in the affirmative
and for type D in the negative. The main tool is a combinatorial two row m
odel for a totally asymmetric simple exclusion process called the D∗-TAS
EP\, with four parameters. By specializing the parameters in different way
s\, we obtain TASEPs for each of the Weyl groups mentioned above\, i.e. on
signed permutations. Computing certain correlations in these TASEPs gives
the desired limiting directions. We also state several explicit conjectur
es for certain probabilities in these TASEPs on signed permutations.\nJoin
t work with Erik Aas\, Arvind Ayyer and Samu Potka.\n
LOCATION:https://stable.researchseminars.org/talk/BIRS-21w5511/5/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Olya Mandelshtam (University of Waterloo)
DTSTART:20210921T170000Z
DTEND:20210921T174500Z
DTSTAMP:20260404T041857Z
UID:BIRS-21w5511/6
DESCRIPTION:by Olya Mandelshtam (University of Waterloo) as part of BIRS w
orkshop: Permutations and Probability\n\nAbstract: TBA\n
LOCATION:https://stable.researchseminars.org/talk/BIRS-21w5511/6/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Gady Kozma (Weizmann Institute)
DTSTART:20210922T150000Z
DTEND:20210922T154500Z
DTSTAMP:20260404T041857Z
UID:BIRS-21w5511/7
DESCRIPTION:Title: Mixing time\, quasi isometries and Cayley graphs\nby Gady
Kozma (Weizmann Institute) as part of BIRS workshop: Permutations and Prob
ability\n\n\nAbstract\nWe show that the (usual\, total variation) mixing t
ime is not a quasi-isometry invariant\, even between Cayley graphs. All te
rms will be explained in the talk. Joint work with Jonathan Hermon.\n
LOCATION:https://stable.researchseminars.org/talk/BIRS-21w5511/7/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Peter Winkler (Dartmouth College)
DTSTART:20210922T161500Z
DTEND:20210922T170000Z
DTSTAMP:20260404T041857Z
UID:BIRS-21w5511/8
DESCRIPTION:Title: Permutons\nby Peter Winkler (Dartmouth College) as part of
BIRS workshop: Permutations and Probability\n\n\nAbstract\nWhat do large
permutations look like? We can in some cases answer this question with\nt
he help of limit structures called "permutons\," and a variational princip
le.\n Examples show nice apparent behavior and some contrasts to the cas
e of graphs and graphons.\nJoint work with Rick Kenyon\, Dan Kral' and Cha
rles Radin\; later\, with Chris Coscia\, Sayan Das\,\n
LOCATION:https://stable.researchseminars.org/talk/BIRS-21w5511/8/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Mathilde Bouvel (CNRS)
DTSTART:20210923T150000Z
DTEND:20210923T154500Z
DTSTAMP:20260404T041857Z
UID:BIRS-21w5511/9
DESCRIPTION:Title: Random permutations biased according to their records\nby
Mathilde Bouvel (CNRS) as part of BIRS workshop: Permutations and Probabil
ity\n\nAbstract: TBA\n
LOCATION:https://stable.researchseminars.org/talk/BIRS-21w5511/9/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Svante Janso (Uppsala University)
DTSTART:20210923T161500Z
DTEND:20210923T170000Z
DTSTAMP:20260404T041857Z
UID:BIRS-21w5511/10
DESCRIPTION:Title: The number of occurrences of patterns and constrained pattern
s in a random permutation\nby Svante Janso (Uppsala University) as par
t of BIRS workshop: Permutations and Probability\n\n\nAbstract\nA pattern
$\\tau$ is a fixed (short) permutation. We are interested in the\nnumber o
f occurrences of a pattern $\\tau$ in a random (long) permutation\n$\\pi$\
, where an occurrence is a subsequence with the same relative order as\n$\
\tau$. We also consider constrained cases\, where we count only occurrence
s\nwith some restrictions on the gaps between the elements of the subseque
nce.\nIn particular\, we consider vincular patterns\, where some elements
in the\nsubsequence are required to be adjacent in $\\pi$.\n\nAsymptotic n
ormality has been shown by Bóna (2007\, 2008\, 2010) and (vincular permut
ations) Hofer (2018). We show that these results follow from\ngeneral resu
lts on U-statistics. For constrained (e.g. vincular) cases\, this\nrequire
s results on m-dependent U-statistics.\n\nWe consider also linear combinat
ions of counts for several patterns.\nTypically\, these too are asymptotic
ally normal\, but there are degenerate\ncases\, see Janson\, Nakamura and
Zeilberger (2015) and Even-Zohar (2020).\nMuch is known about degenerate c
ases too\, but there are also open problems\,\nin particular for constrain
ed cases.\n
LOCATION:https://stable.researchseminars.org/talk/BIRS-21w5511/10/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Lucas Teyssier (Universität Wien)
DTSTART:20210924T150000Z
DTEND:20210924T154500Z
DTSTAMP:20260404T041857Z
UID:BIRS-21w5511/11
DESCRIPTION:Title: Cutoff profile for random transpositions\nby Lucas Teyssi
er (Universität Wien) as part of BIRS workshop: Permutations and Probabil
ity\n\n\nAbstract\nThe representation theory of the symmetric group provid
es several beautiful combinatorial formulas. The idea to use it to study r
andom walks comes from Diaconis and Shahshahani\, who used some formulas t
o bound the eigenvalues of the random transposition shuffle\, leading to a
cutoff phenomenon. Our main goal will be to explain how to improve their
L^2 bound method to obtain cutoff profiles\, and more concretely how this
applies to random transpositions.\n
LOCATION:https://stable.researchseminars.org/talk/BIRS-21w5511/11/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Alexander Holroyd (University of Bristol)
DTSTART:20210924T161500Z
DTEND:20210924T170000Z
DTSTAMP:20260404T041857Z
UID:BIRS-21w5511/12
DESCRIPTION:by Alexander Holroyd (University of Bristol) as part of BIRS w
orkshop: Permutations and Probability\n\nAbstract: TBA\n
LOCATION:https://stable.researchseminars.org/talk/BIRS-21w5511/12/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Lauren Williams (Harvard University)
DTSTART:20210924T170000Z
DTEND:20210924T174500Z
DTSTAMP:20260404T041857Z
UID:BIRS-21w5511/13
DESCRIPTION:Title: Schubert polynomials\, the inhomogeneous TASEP\, and evil-avo
iding permutations\nby Lauren Williams (Harvard University) as part of
BIRS workshop: Permutations and Probability\n\n\nAbstract\nThe totally as
ymmetric simple exclusion process (TASEP) was introduced around 1970 as a
model for translation in protein synthesis and traffic flow. The inhomogen
eous TASEP is a Markov chain of weighted particles hopping on a lattice\,
in which the hopping rate depends on the weight of the particles being int
erchanged. We will consider the case where the lattice is a ring\, and eac
h particle has a distinct weight\, so that we can think of this model as a
Markov chain on permutations. We will see that in many cases\, and in par
ticular for w an "evil-avoiding" permutation\, the steady state probabilit
y of w can be expressed in terms of Schubert polynomials. Based on joint w
ork with Donghyun Kim. The inhomogeneous TASEP\, Schubert polynomials\, an
d evil-avoiding permutations\n
LOCATION:https://stable.researchseminars.org/talk/BIRS-21w5511/13/
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