A random matrix approach to the Peterson-Thom conjecture
Operator Algebras
2022-03-15 v2 Functional Analysis
Probability
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.
Cite
@article{arxiv.2008.12287,
title = {A random matrix approach to the Peterson-Thom conjecture},
author = {Ben Hayes},
journal= {arXiv preprint arXiv:2008.12287},
year = {2022}
}
Comments
46 pages. This is the final version, and will appear as such in the Indiana University Mathematics Journal