AG Mathematische Stochastik : Jana Reker

Datum: 14-06-2023Zeit: 16:15 – 18:15Ort: 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.

https://www.math.fau.de/stochastik/oberseminar-stochastik/

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Details

Datum:
14-06-2023
Zeit:
16:15 – 18:15
Ort:

Raum : 04.363

Veranstaltungskategorien:
Oberseminar Stochastik