LONG TIME BEHAVIOR OF THE TRANSITION PROBABILITY OF A RANDOM WALK WITH DRIFT ON AN ABELIAN COVERING GRAPH

Abstract

For a certain class of reversible random walks possibly with drift on an abelian covering graph of a finite graph, using the technique of twisted transition operator, we obtain the asymptotic behavior of the $n$-step transition probability $p_n(x,y)$ as $n\to\infty$ and give an expression of the constant which appears in the asymptotics.