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Spectral gaps for random Schreier graphs

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OGGW03 - Spectral gaps

I will discuss a generalization of Friedman’s theorem, focusing on the spectral gap of the random regular Schreier graphs associated with the action of S_n on K_n—tuples of distinct elements in {1,...,n}. The proof relies on the `polynomial method’, a new approach to strong convergence of Chen, Garza—Vargas, Tropp and van Handel, combined with new group theoretic inputs. A key ingredient is a new asymptotic bound on the expected character of a random permutation obtained via a word map, which is expressed in terms of the dimension of the corresponding representation. 

This talk is part of the Isaac Newton Institute Seminar Series series.

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in person & via zoom CMS, Meeting Room 15 Room 5, Cripps Court, Magdalene College (Chesterton Road)

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