QLunch: Jacob Fronk

Speaker: Jacob Fronk from QMATH

Title: Norm Convergence for Polynomials of Random Matrices 

Abstract: 

We study a general class of Hermitian non-commutative quadratic polynomials of multiple independent Wigner matrices. We establish that, as the dimension N of the matrices grows to infinity, the operator norm of such polynomials q converges to a deterministic limit and we prove an optimal rate of convergence of N^(-2/3+o(1)).

To obtain the result we study the limit of the eigenvalue density of q. We prove that this density always has a square root growth at its edges and show that combining this with an optimal local law leads to the desired rate of convergence. This is joint work with my PhD advisor Torben Krüger.