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SUMMARY:Marek Biskup (UCLA)
DTSTART:20200608T140000Z
DTEND:20200608T150000Z
DTSTAMP:20260422T225818Z
UID:MunichProbabilitySeminar/1
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/MunichProbab
 ilitySeminar/1/">A quenched invariance principle for random walks with lon
 g range jumps</a>\nby Marek Biskup (UCLA) as part of Munich Probability Se
 minar\n\n\nAbstract\nI will discuss random walks among random conductances
  on the hypercubic lattice that allow for jumps of arbitrary length. This 
 includes the random walk on the long-range percolation graph obtained by a
 dding to $\\mathbb Z^d$ an edge between $x$ and $y$ with probability propo
 rtional to $|x-y|^{-s}$\, independently of other pairs of vertices. By a c
 ombination of functional inequalities and location-dependent truncations\,
  I will prove that the random walk scales to Brownian motion under a diffu
 sive scaling of space and time. The proof follows the usual route of reduc
 ing the statement to everywhere sublinearity of the corrector. We prove th
 e latter under moment conditions on the environment that in fact turn out 
 to be more or less necessary for the method of proof. For the above percol
 ation problem\, this requires the exponent~$s$ to exceed~$2d$. Based on jo
 int work with X. Chen\, T. Kumagai and J. Wang.\n
LOCATION:https://researchseminars.org/talk/MunichProbabilitySeminar/1/
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