Browsing SUNY Plattsburgh by Subject "Martin boundary"

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Amenability and superharmonic functions

Northshield, Sam (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 ...
On the spectrum and Martin boundary of homogeneous spaces

Northshield, Sam (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 ...