Stochastic Box-Ball System - Convergence to Brownian Motion
Offered By: Institute for Pure & Applied Mathematics (IPAM) via YouTube
Course Description
Overview
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)
Related Courses
Introduction to Probability, Statistics, and Random ProcessesUniversity of Massachusetts Amherst via Independent Stochastic Processes
Indian Institute of Technology Delhi via Swayam Introduction to Polymer Physics-IITR
Indian Institute of Technology Roorkee via Swayam Path Integral Methods in Physics & Finance
Indian Institute of Technology Roorkee via Swayam Biophysical Chemistry
NPTEL via YouTube