ON SPECTRAL PROPERTIES OF THE SCHREIER GRAPHS OF THE THOMPSON GROUP F Academic Article uri icon

abstract

  • In this article we study spectral properties of the family of Schreier graphs associated to the action of the Thompson group F F on the interval [ 0 , 1 ] [0,1] . In particular, we describe spectra of Laplace type operators associated to these Schreier graphs and calculate certain spectral measures associated to the Schreier graph Upsilon of the orbit of 1 / 2 1/2 . As a byproduct we calculate the asymptotics of the return probabilities of the simple random walk on Upsilon starting at 1 / 2 1/2 . In addition, given a Laplace type operator L L on a tree-like graph we study relations between the spectral measures of L L associated to delta functions of different vertices and the spectrum of L L .

published proceedings

  • TRANSACTIONS OF THE AMERICAN MATHEMATICAL SOCIETY

author list (cited authors)

  • Dudko, A., & Grigorchuk, R.

complete list of authors

  • Dudko, Artem||Grigorchuk, Rostislav

publication date

  • 2023