##### Department of Mathematics,

University of California San Diego

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### Math 288 - Probability Seminar

## Dr. Kevin Yang

#### UC Berkeley

## Stochastic PDEs arising from stochastic Laplacian growth in non-Markovian diffusions

##### Abstract:

The analysis of non-Markovian, self-interacting diffusions, which has motivations from probability, physics, biology, etc., is intimately connected with that of an associated stochastic interface. In this talk, we will look at dynamical fluctuations of this interface, and derive a KPZ-type stochastic PDE as a scaling limit. Unlike the usual KPZ equation, the geometry of the underlying manifold plays an important role in the analysis of this SPDE. Deriving the SPDE from the diffusion model is based on a novel "local-to-global" stochastic homogenization principle. Studying the SPDE itself amounts to relatively modern ideas in stochastic analysis coupled with analysis of pseudo-differential operators on manifolds. Based on joint work with Amir Dembo.

### May 11, 2023

### 11:00 AM

APM 6311 with live streaming via Zoom.

Contact poagarwal@ucsd.edu for Zoom info

Research Areas

Probability Theory****************************