AG Mathematische Stochastik : Jana Reker

Jun 14
14-06-2023 16:15 Uhr bis 18:15 Uhr
Raum : 04.363

Title: Functional Central Limit Theorems for Wigner Matrices

Consider the random variable X := Tr(f1(W )A1 . . . fk(W )Ak) where
W is a Hermitian Wigner matrix, k ∈ N, and we choose regular func-
tions f1, . . . , fk as well as bounded deterministic matrices A1, . . . , Ak. In
this talk, we study the fluctuations around EX and give a functional central
limit theorem on macroscopic and mesoscopic scales. Analyzing the under-
lying combinatorics further leads to explicit formulas for the variance of X
as well as the covariance of X and Y := Tr(fk+1(W )Ak+1 . . . fk+ℓ(W )Ak+ℓ)
of similar build. The results obtained match the structure of formulas in
second-order free probability which were previously only available for fj be-
ing polynomials.