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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 ...