Recurrence and Transience on Random Graphs

Student: Gilyov Dmitriy

Educational Programme: Mathematics (Bachelor)

Year of Graduation: 2021

In the thesis we consider Markov processes on a graph and study how fast the original random walk converges to the equilibrium distribution in comparison with it's symmetrical part. The goal of this paper is to prove that a rate of convergence of symmetrical part of a random walk is not higher than a rate of the initial random walk and to find conditions under which a non-reversible random walk converges to it's invariant distribution faster than it's symmetrical part. These conditions may give a hint for constructing faster sampling MCMC algorithms.

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