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from Part II - Results and Applications
Published online by Cambridge University Press: 16 May 2024
In this chapter we start applying the tools developed in Part I to study random walks.The notion of amenable groups is defined, and Kesten’s criterion for amenable groups is proved. We then move to define the notion of isopermitric dimension. Inequalities relating the volume growth of a group to the isoperimetric dimension and to the decay of the heat kernel are proved.
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