POLYNOMIAL CONVERGENCE TO EQUILIBRIUM FOR A SYSTEM OF INTERACTING PARTICLES

• 成果类型: Article
• 署名作者: Li, Yao; Young, Lai-Sang
• 署名单位: University of Massachusetts System; University of Massachusetts Amherst; New York University
• 刊物名称: ANNALS OF APPLIED PROBABILITY
• ISSN/ISSBN: 1050-5164
• DOI: 10.1214/16-AAP1197
• 发表日期: 2017
• 页码: 65-90
• 关键词: large deviations; spectral gap; subgeometric rates; simple-model; ergodicity; transport; equation; heat

摘要

We consider a stochastic particle system in which a finite number of particles interact with one another via a common energy tank. Interaction rate for each particle is proportional to the square root of its kinetic energy, as is consistent with analogous mechanical models. Our main result is that the rate of convergence to equilibrium for such a system is similar to t(-2), more precisely it is faster than a constant times t(-2+epsilon) for any epsilon > 0. A discussion of exponential vs. polynomial convergence for similar particle systems is included.