Cycle symmetries and circulation fluctuations for discrete-time and continuous-time Markov chains

Chen Jia; Daquan Jiang; Minping Qian

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arXiv · 1407.1263

Cycle symmetries and circulation fluctuations for discrete-time and continuous-time Markov chains

Chen Jia·Daquan Jiang·Minping Qian

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Abstract

In probability theory, equalities are much less than inequalities. 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 empirical circulations of a family of cycles passing through a common state satisfy a large deviation principle with a rate function which has an highly non-obvious symmetry. Finally, we discuss the applications of our work in statistical physics and biochemistry.

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Chen Jia, Daquan Jiang, Minping Qian. 2014-07-18. Cycle symmetries and circulation fluctuations for discrete-time and continuous-time Markov chains. https://arxiv.org/abs/1407.1263

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