Academic Editor: Youssef EL FOUTAYENI
Received |
Accepted |
Published |
21 January 2020 |
05 February 2020 |
10 March 2020 |
Abstract: In mathematics, an amenable group is a locally compact topological group G carrying a kind of averaging operation on bounded functions that is invariant under translation by group elements. The original definition, in terms of a finitely additive invariant measure (or mean) on subsets of G, was introduced by John von Neumann in 1929 (see [1]) in response to the Banach–Tarski paradox. The amenability property has a large number of equivalent formulations. In 1959, Harry Kesten (see [2]) proved that there is a relation between the amenability and the estimates of symmetric random walk on finitely generated groups. The concept of amenability, has been central in many areas of mathematics and in several fields (see for example [3,4,5,6]} or more recently [7,8]. In this work we study this relation according to return probability to the origin. Our aim is to study the amenability of sofic groups using Return Probability.
