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 M3//EN
VERSION:2.0
CALSCALE:GREGORIAN
METHOD:PUBLISH
BEGIN:VEVENT
DTSTAMP:20210210T180856Z
DTSTART:20210217T150000Z
DTEND:20210217T160000Z
SUMMARY:Peter Taylor -  Limiting Behaviour for Heat Kernels of Random Pro
 cesses in Random Environments
UID:{http://www.columbasystems.com/customers/uom/gpp/eventid/}z1j4-kkzqyr
 8z-yptj9d
DESCRIPTION:Peter Taylor (Cambridge) will speak in the Probability semina
 r. \n\nIn this talk I will present recent results on random processes mo
 ving in random environments.\n\nIn the first part of the talk\, we intro
 duce the Random Conductance Model (RCM)\; a random walk on an infinite l
 attice (usually taken to be $\\mathbb{Z}^d$) whose law is determined by 
 random weights on the (nearest neighbour) edges. In the setting of degen
 erate\, ergodic weights and general speed measure\, we present a local l
 imit theorem for this model which tells us how the heat kernel of this p
 rocess has a Gaussian scaling limit. Furthermore\, we exhibit applicatio
 ns of said local limit theorems to the Ginzburg-Landau gradient model. T
 his is a model for a stochastic interface separating two distinct thermo
 dynamic phases\, using an infinite system of coupled SDEs. Based on join
 t work with Sebastian Andres.\n\nIf time permits I will define another p
 rocess - symmetric diffusion in a degenerate\, ergodic medium. This is a
  continuum analogue of the above RCM and the techniques take inspiration
  from there. We show upper off-diagonal (Gaussian-like) heat kernel esti
 mates\, given in terms of the intrinsic metric of this process\, and a s
 caling limit for the Green's kernel.
STATUS:TENTATIVE
TRANSP:TRANSPARENT
CLASS:PUBLIC
LOCATION:https://zoom.us/j/99553510079
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