# On spectral properties of the Schreier graphs of the Thompson group $F$

@inproceedings{Dudko2021OnSP, title={On spectral properties of the Schreier graphs of the Thompson group \$F\$}, author={Artem Dudko and Rostislav I. Grigorchuk}, year={2021} }

The Thompson’s group F is one of the most famous and most important groups related to many areas of mathematics (see the survey [3]). The question about amenability of this group remains open for more than 50 years despite many attempts to solve it. By a remarkable Kesten’s criterion of amenability a group G is amenable if and only if 1 belongs to the spectrum of the Markov operator associated to a symmetric random walk on G. This criterion also holds for graphs of uniformly bounded degree (see…

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