A random matrix approach to the Peterson-Thom conjecture

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