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On the spectrum and Martin boundary of homogeneous spaces
(Statistics and Probability Letters, 1995)
Given a conservative, spatially homogeneous Markov process X on an homogeneous spaces χ, we show that if the bottom of the spectrum of the generator of X is zero then the Martin boundary of contains a unique point fixed ...
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 ...