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SUMMARY:Limiting Behaviour for Heat Kernels of Random Processes in Random 
  Environments - Peter Taylor (Statslab)
DTSTART:20210216T140000Z
DTEND:20210216T150000Z
UID:TALK157480@talks.cam.ac.uk
CONTACT:Perla Sousi
DESCRIPTION:In this talk I will present recent results on random processes
  moving in \nrandom environments.\n\nIn the first part of the talk\, we in
 troduce the Random Conductance Model \n(RCM)\; a random walk on an infinit
 e lattice (usually taken to be \n$\\mathbb{Z}^d$) whose law is determined 
 by random weights on the \n(nearest neighbour) edges. In the setting of de
 generate\, ergodic weights \nand general speed measure\, we present a loca
 l limit theorem for this \nmodel which tells us how the heat kernel of thi
 s process has a Gaussian \nscaling limit. Furthermore\, we exhibit applica
 tions of said local limit \ntheorems to the Ginzburg-Landau gradient model
 . This is a model for a \nstochastic interface separating two distinct the
 rmodynamic phases\, using \nan infinite system of coupled SDEs. Based on j
 oint work with Sebastian \nAndres.\n\nIf time permits I will define anothe
 r process - symmetric diffusion in a \ndegenerate\, ergodic medium. This i
 s a continuum analogue of the above \nRCM and the techniques take inspirat
 ion from there. We show upper \noff-diagonal (Gaussian-like) heat kernel e
 stimates\, given in terms of \nthe intrinsic metric of this process\, and 
 a scaling limit for the \nGreen's kernel.
LOCATION:Zoom
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