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

2014/07/04 by Jia, Chen, Jiang, Daquan, Qian, Minping · 1 citation
#60F10 #60J10 #60J20 #60J27 #60J28 #FOS: Mathematics #Probability (math.PR)

paper · doi:10.48550/arxiv.1407.1263

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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