Browsing Mathematics Faculty Work by Subject "random walk"
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Amenability and superharmonic functions
(Proceedings of the American Mathematical Society, 1993)Let G be a countable group and u a symmetric and aperiodic probability measure on G . We show that G is amenable if and only if every positive superharmonic function is nearly constant on certain arbitrarily large subsets ... 
Cogrowth of Regular Graphs
(Proceedings of the American Mathematical Society, 1992)Let G be a dregular graph and T the covering tree of G. We define a cogrowth constant of G in T and express it in terms of the first eigenvalue of the Laplacian on G. As a corollary, we show that the cogrowth constant is ...