ON THE POLYNOMIAL CONVERGENCE RATE TO NONEQUILIBRIUM STEADY STATES

• 成果类型: Article
• 署名作者: Li, Yao
• 署名单位: University of Massachusetts System; University of Massachusetts Amherst
• 刊物名称: ANNALS OF APPLIED PROBABILITY
• ISSN/ISSBN: 1050-5164
• DOI: 10.1214/18-AAP1406
• 发表日期: 2018
• 页码: 3765-3812
• 关键词: heat-conduction; anharmonic chains; particle-systems; energy-exchange; markov-chains; fouriers law; MODEL; decay; billiards; driven

摘要

We consider a stochastic energy exchange model that models the 1-D microscopic heat conduction in the nonequilibrium setting. In this paper, we prove the existence and uniqueness of the nonequilibrium steady state (NESS) and, furthermore, the polynomial speed of convergence to the NESS. Our result shows that the asymptotic properties of this model and its deterministic dynamical system origin are consistent. The proof uses a new technique called the induced chain method. We partition the state space and work on both the Markov chain induced by an active set and the tail of return time to this active set.