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Central limit theorems for random matrices: From resolvents to free probability
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 choose (possibly N-dependent) regular functions f1, . . . , fk as well as bounded deterministic matrices A1, . . . ,
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