Yue Wang, Department of Applied Math, Univ of Washington

SMI 304
With the help of algebraic topology and graph theory, we prove that a finite Markov chain can be lifted into an infinite Markov chain with proper global potential. Or equivalently, we can embed a finite Markov chain into ntorus, such that two paths are homotopy equivalent if and only if they have the same potential gain. For the lifted Markov chain, we prove that its entropy production rate will converge to that of the original Markov chain in Cesaro's sense. Most of the above results are also valid for diffusion processes on ntorus. This is a joint work with Prof. Hong Qian.