Random walks on the triangular prism and other vertex-transitive graphs

摘要

In this paper we consider Markov chains of the following type: the state space is the set of vertices of a connected, regular graph, and for each vertex transitions are to the adjacent vertices, which equal probabilities. The proof is given that the mean first-passage matrix F of such a Markov chain is symmetric, when the underlying graph is vertex-transitive. Hence, we can apply results from a previous paper, in which we investigated general, finite, ergodic Markov chains, with the property F= FT.