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Abstract In 1959, Harry Kesten proved that there is a relation between the amenability and the estimates of symmetric random walk on finitely generated groups. Our aim is to give… Click to show full abstract
Abstract In 1959, Harry Kesten proved that there is a relation between the amenability and the estimates of symmetric random walk on finitely generated groups. Our aim is to give a generalization of the Kesten’s characterization for locally compact groups. We prove that the probability to return to the origin after 2n steps decays like exp(–n). In addition, we give an answer to the question that is conjectured in [9] related to the comparison between the probabilities of return on a locally compact group and on one of its subgroups.
Keywords:
return origin;
locally compact;
amenability;
probability return;
compact groups
Journal Title: Journal of Interdisciplinary Mathematics
Year Published: 2020
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Journal Title: Journal of Interdisciplinary Mathematics
Year Published: 2020
Link to full text (if available)
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recommendations!