A random matrix approach to the Peterson-Thom conjecture

By Ben Hayes. Indiana University Mathematics Journal, 2020

48 citations recorded by the source corpus.

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.

Subfields: Geometry and Topology, Mathematical Physics, Statistics and Probability

View Paper: https://www.semanticscholar.org/paper/7bf7be27f73ba03c775bd8663f71e70fdb66f661

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In Geometry and Topology

1. Ramon van Handel
2. Afonso S. Bandeira

In Mathematical Physics

1. Afonso S. Bandeira
2. March Boedihardjo
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4. Justin Salez
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6. Marcel Nutz
7. Nicholas A. Cook
8. Nicole El Karoui

Citations in the corpus

• Matrix concentration inequalities and free probability (2021, background): “In the recent work [22], it was shown that if strong convergence”