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Examples of noncommutative groups with nontrivial exit-boundary

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Abstract

A number of new counterexamples are given, disproving certain assumptions about the mutual relations of the exit-boundary (Poisson boundary) of a random walk on a group and the amenability and growth of the group. Random walks are constructed with nontrivial exit-boundary on the affine group of the dyadic-rational line and on the infinite symmetric group.

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Authors
  1. V. A. Kaimanovich
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Translated from Zapiski Nauchnykh Seminarov Leningradskogo Otdeleniya Matematicheskogo Instituta im. V. A. Steklova AN SSSR, Vol. 123, pp. 167–184, 1983.

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Kaimanovich, V.A. Examples of noncommutative groups with nontrivial exit-boundary. J Math Sci 28, 579–591 (1985). https://doi.org/10.1007/BF02104988

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