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February 2001 Spectral gap for Kac's model of Boltzmann equation
Elise Janvresse
Ann. Probab. 29(1): 288-304 (February 2001). DOI: 10.1214/aop/1008956330

Abstract

We consider a random walk on $S^{n-1}$ , the standard sphere of dimension $n -1$, generated by random rotations on randomly selected coordinate planes $i,j$ with $1 \le i < j \le n$. This dynamic was used by Marc Kac as a model for the spatially homogeneous Boltzmann equation. We prove that the spectral gap on $S^{n-1}$ is $n^{-1}$ up to a constant independent of $n$.

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Elise Janvresse. "Spectral gap for Kac's model of Boltzmann equation." Ann. Probab. 29 (1) 288 - 304, February 2001. https://doi.org/10.1214/aop/1008956330

Information

Published: February 2001
First available in Project Euclid: 21 December 2001

zbMATH: 1034.82049
MathSciNet: MR1825150
Digital Object Identifier: 10.1214/aop/1008956330

Subjects:
Primary: 60K35

Rights: Copyright © 2001 Institute of Mathematical Statistics

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Vol.29 • No. 1 • February 2001
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