D. George

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math.PR2025

Ultra high order cumulants and quantitative CLT for polynomials in Random Matrices

Zhigang Bao, Daniel Munoz George

From the study of the high order freeness of random matrices, it is known that the order $r$ cumulant of the trace of a polynomial of $N$ -dimensional GUE/GOE is of order $N^{2 - r}$ …

math.PR2025

Asymptotic limit of cumulants and higher order free cumulants of complex Wigner matrices

James A. Mingo, Daniel Munoz George

We compute the fluctuation moments $I^\pm_{m_{1}, \dots, m_{r}}$ of a Complex Wigner Matrix $X_{N}$ given by the limit $lim_{N \to \infty} N^{r - 2} k_{r} (T r (X_{N}^{m_{1}}), \dots, T r (X_{N}^{m_{r}}))$ …