Bounds for Kac's master equation
type: Item
instance of: scholarly article
title: Bounds for Kac's master equation
zbMATH Open document ID: 0953.60098
author: Persi Diaconis
author: Laurent Saloff-Coste
published in: Communications in Mathematical Physics
publication date: 2001-01-29T00:00:00Z
review text: The authors consider a random walk on the orthogonal group SO\((n)\) which was firstly introduced by M. Kac to study Boltzmann's derivation of a basic equation of kinetic theory. The random walk describes a system of velocities for which the total energy is conserved -- hence the restriction to the sphere. It is a Markov chain on the \(n\)-sphere based on random rotations in randomly chosen coordinate planes. This random walk has also been studied by Hastings as a simple way of generating an approximately random equation. The present authors show that the walk has a spectral gap bounded below by \(c/n^3\). They use this result and curvature information to bound the rate of convergence to stationarity.
Mathematics Subject Classification ID: 60K40
Mathematics Subject Classification ID: 82C41
Mathematics Subject Classification ID: 82C40
Mathematics Subject Classification ID: 60G50
zbMATH DE Number: 1422937
zbMATH Keywords: master equation
zbMATH Keywords: random walk
reviewed by: Sylvie Méléard
MaRDI profile type: Publication
full work available at URL: s002200050036
OpenAlex ID: W1991977420
DOI: 10.1007/S002200050036
description: scientific article; zbMATH DE number 1422937