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.
Tohoku Math. J. (2)
55(2):
255-269
(2003).
DOI: 10.2748/tmj/1113246940
