CYCLE SYMMETRIES AND CIRCULATION FLUCTUATIONS FOR DISCRETE-TIME AND CONTINUOUS-TIME MARKOV CHAINS

• 成果类型: Article
• 署名作者: Jia, Chen; Jiang, Da-Quan; Qian, Min-Ping
• 署名单位: Chinese Academy of Engineering Physics; Beijing Computational Science Research Center (CSRC); Peking University; Peking University
• 刊物名称: ANNALS OF APPLIED PROBABILITY
• ISSN/ISSBN: 1050-5164
• DOI: 10.1214/15-AAP1152
• 发表日期: 2016
• 页码: 2454-2493
• 关键词: network; THEOREM; probability; EQUALITY; BEHAVIOR

摘要

In this paper, we find a series of equalities which characterize the symmetry of the forming times of a family of similar cycles for discrete-time and continuous-time Markov chains. Moreover, we use these cycle symmetries to study the circulation fluctuations for Markov chains. We prove that the sample circulations along a family of cycles passing through a common state satisfy a large deviation principle with a rate function which has a highly nonobvious symmetry. Further extensions and applications to statistical physics and biochemistry are also discussed, especially the fluctuation theorems for the sample net circulations.