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arXiv · 2008.12287

A random matrix approach to the Peterson-Thom conjecture

Ben Hayes
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Abstract

The Peterson-Thom conjecture asserts that any diffuse, amenable subalgebra of a free group factor is contained in a unique maximal amenable subalgebra. This conjecture is motivated by related results in Popa's deformation/rigidity theory and Peterson-Thom's results on L^{2}-Betti numbers. We present an approach to this conjecture in terms of so-called strong convergence of random matrices by formulating a conjecture which is a natural generalization of the Haagerup-Thorbjornsen theorem whose validity would imply the Peterson-Thom conjecture. This random matrix conjecture is related to recent work of Collins-Guionnet-Parraud.

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Ben Hayes. 2020-08-27. A random matrix approach to the Peterson-Thom conjecture. https://arxiv.org/abs/2008.12287

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