Peter Taylor - Limiting Behaviour for Heat Kernels of Random Processes in Random Environments
| Dates: | 17 February 2021 |
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| Times: | 15:00 - 16:00 |
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| What is it: | Seminar |
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| Organiser: | Department of Mathematics |
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| Speaker: | Peter Taylor |
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Peter Taylor (Cambridge) will speak in the Probability seminar.
In this talk I will present recent results on random processes moving in random environments.
In the first part of the talk, we introduce the Random Conductance Model (RCM); a random walk on an infinite lattice (usually taken to be $\mathbb{Z}^d$) whose law is determined by random weights on the (nearest neighbour) edges. In the setting of degenerate, ergodic weights and general speed measure, we present a local limit theorem for this model which tells us how the heat kernel of this process has a Gaussian scaling limit. Furthermore, we exhibit applications of said local limit theorems to the Ginzburg-Landau gradient model. This is a model for a stochastic interface separating two distinct thermodynamic phases, using an infinite system of coupled SDEs. Based on joint work with Sebastian Andres.
If time permits I will define another process - 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 estimates, given in terms of the intrinsic metric of this process, and a scaling limit for the Green's kernel.
Travel and Contact Information
Find event
https://zoom.us/j/99553510079
