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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 d-regular 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 ...