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math.PR2022
Quantitative Estimates for Operator-Valued and Infinitesimal Boolean and Monotone Limit Theorems
Octavio Arizmendi, Marwa Banna, Pei-Lun Tseng
We provide Berry-Esseen bounds for sums of operator-valued Boolean and monotone independent variables, in terms of the first moments of the summands. Our bounds are on the level of…
math.PR2022
Asymptotic free independence and entry permutations for Gaussian random matrices. Part II: Infinitesimal freeness
M. Popa, K. Szpojankowski, P. -L. Tseng
We study asymptotic infinitesimal distributions of Gaussian Unitary Ensembles with permuted entries. We show that for random uniform permutations, the asymptotically permuted GUE m…
math.OA2022★ 1 cited
Operator-Valued Infinitesimal Multiplicative Convolutions
Pei-Lun Tseng
We consider the notions of operator-valued infinitesimal (OVI) free independence, OVI Boolean independence, and OVI monotone independence. For each notion of OVI independence, we i…