Multi-point functional central limit theorem for Wigner matrices
J Reker - Electronic Journal of Probability, 2024 - projecteuclid.org
Consider the random variable Tr (f 1 (W) A 1… fk (W) A k) where W is an N× N Hermitian
Wigner matrix, k∈ ℕ, and choose (possibly N-dependent) regular functions f 1,…, fk as well …
Wigner matrix, k∈ ℕ, and choose (possibly N-dependent) regular functions f 1,…, fk as well …
Fluctuation Moments for Regular Functions of Wigner Matrices
J Reker - Mathematical Physics, Analysis and Geometry, 2024 - Springer
We compute the deterministic approximation for mixed fluctuation moments of products of
deterministic matrices and general Sobolev functions of Wigner matrices. Restricting to …
deterministic matrices and general Sobolev functions of Wigner matrices. Restricting to …
Central limit theorems for random matrices: From resolvents to free probability
J Reker - 2024 - research-explorer.ista.ac.at
This thesis is structured into two parts. In the first part, we consider the random variable X:=
Tr (f1 (W) A1... fk (W) Ak) where W is an N× N Hermitian Wigner matrix, k∈ N, and we …
Tr (f1 (W) A1... fk (W) Ak) where W is an N× N Hermitian Wigner matrix, k∈ N, and we …
Second order cumulants: Second order even elements and -diagonal elements
O Arizmendi, JA Mingo - Annales de l'Institut Henri Poincaré D, 2023 - ems.press
We introduce R-diagonal and even operators of second order. We give a formula for the
second order free cumulants of the square x2 of a second order even element in terms of the …
second order free cumulants of the square x2 of a second order even element in terms of the …