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Stochastic Box-Ball System - Convergence to Brownian Motion

Offered By: Institute for Pure & Applied Mathematics (IPAM) via YouTube

Tags

Probability Theory Courses Combinatorics Courses Mathematical Modeling Courses Statistical Mechanics Courses Brownian Motion Courses

Course Description

Overview

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Explore the stochastic version of the box-ball system in this 40-minute lecture presented by David Keating from the University of Wisconsin-Madison at IPAM's Vertex Models workshop. Delve into the deterministic discrete-time dynamical system introduced by Takahashi and Satsuma, where boxes at each natural number can hold a single ball or be empty. Discover how the introduction of a failure probability ϵ transforms the system into a stochastic model. Examine the focus on inter-distance configurations rather than individual ball positions, and learn about the main result showing convergence to semi-martingale reflecting Brownian motion after suitable rescaling. Gain insights into this fascinating topic at the intersection of pure and applied mathematics.

Syllabus

David Keating - Stochastic Box-Ball System - IPAM at UCLA


Taught by

Institute for Pure & Applied Mathematics (IPAM)

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