##### Department of Mathematics,

University of California San Diego

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### Math 288 - Probability & Statistics

## Prof. David Weisbart

#### UC Riverside

## $p$-Adic Brownian Motion is a Scaling Limit

##### Abstract:

The Laplace operator is the infinitesimal generator of Brownian motion with a real state space. The Vladimirov operator, a $p$-adic analogue of the Laplace operator, similarly gives rise to Brownian motion with a $p$-adic state space. This talk aims to introduce the concept of a $p$-adic Brownian motion and demonstrate a further similarity with its real analogue: $p$-adic Brownian motion is a scaling limit of a discrete-time random walk on a discrete group. Attendees need not have prior knowledge of $p$-adic analysis, as the talk will provide a brief review of necessary background information.

### May 30, 2024

### 11:00 AM

APM 6402 and zoom: https://ucsd.zoom.us/j/

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