BEGIN:VCALENDAR VERSION:2.0 PRODID:researchseminars.org CALSCALE:GREGORIAN X-WR-CALNAME:researchseminars.org BEGIN:VEVENT SUMMARY:Marek Biskup (UCLA) DTSTART:20200608T140000Z DTEND:20200608T150000Z DTSTAMP:20260404T110831Z UID:MunichProbabilitySeminar/1 DESCRIPTION:Title: A quenched invariance principle for random walks w ith long range jumps\nby Marek Biskup (UCLA) as part of Munich Probabi lity Seminar\n\n\nAbstract\nI will discuss random walks among random condu ctances on the hypercubic lattice that allow for jumps of arbitrary length . This includes the random walk on the long-range percolation graph obtain ed by adding to $\\mathbb Z^d$ an edge between $x$ and $y$ with probabilit y proportional to $|x-y|^{-s}$\, independently of other pairs of vertices. By a combination of functional inequalities and location-dependent trunca tions\, I will prove that the random walk scales to Brownian motion under a diffusive scaling of space and time. The proof follows the usual route o f reducing the statement to everywhere sublinearity of the corrector. We p rove the latter under moment conditions on the environment that in fact tu rn out to be more or less necessary for the method of proof. For the above percolation problem\, this requires the exponent~$s$ to exceed~$2d$. Base d on joint work with X. Chen\, T. Kumagai and J. Wang.\n LOCATION:https://stable.researchseminars.org/talk/MunichProbabilitySeminar /1/ END:VEVENT END:VCALENDAR