Tags → #free probability

Thermalisation for Wigner matrices
We extend key results from free probability on polynomials to arbitrary Sobolev functions. Applied to time Heisenberg evolution operators this proves the thermalization effect of the unitary group generated by Wigner matrices.

Matrix Concentration Inequalities and Free Probability II. Twosided Bounds and Applications
We determine the approximate location of the extreme eigenvalues for a large class of random matrix models. These twosided bounds are fundamentally beyond the reach of classical matrix concentration inequalities.