Zhigang Bao

collaborators

4 papers

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

Numerical Radius of Non-Hermitian Random Matrices

Zhigang Bao, Giorgio Cipolloni

For a square matrix, the range of its Rayleigh quotients is known as the numerical range, which is a compact and convex set by the Toeplitz-Hausdorff theorem. The largest value and…

math.PR2025

Law of fractional logarithm for random matrices

Zhigang Bao, Giorgio Cipolloni, LÃ¡szlÃ³ ErdÅs +2

We prove the Paquette-Zeitouni law of fractional logarithm (LFL) for the extreme eigenvalues [arXiv:1505.05627] in full generality, and thereby verify a conjecture from [arXiv:1505…

math.PR2025

Decorrelation transition in the Wigner minor process

Zhigang Bao, Giorgio Cipolloni, LÃ¡szlÃ³ ErdÅs +2

We consider the Wigner minor process, i.e. the eigenvalues of an $N \times N$ Wigner matrix $H^{(N)}$ together with the eigenvalues of all its $n \times n$ minors, $H^{(n)}$ , $n\le N…