Random walks on trees and Ramanujan graphs

Tatiana Smirnova-Nagnibeda
University of Geneva
Department of Mathematics

I will discuss two instances of how random walks
on infinite trees can be used to study the Ramanujan
property for finite non-regular graphs:

1) construction of infinite trees with infinitely many finite quotients none of which is Ramanujan (joint work with A. Lubotzky);

2) algorithm which decides in finite time whether a given finite graph is Ramanujan.

Presentation (PDF File)

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