D. George

collaborators

5 papers

math.AC2026

Probabilities of random monomial ideals associated to large graphs

Daniel Munoz George, Humberto MuÃ±oz-George, Kevin MuÃ±oz George

Inspired by the ErdÅs RÃ©nyi model, we propose a new model for freesquare random monomial ideals generated by edges and covers of a graph. This permit us to investigate the condit…

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.CO2025

Corrections to Classical Matrix Ensemble Moments, Non-Crossing Annular Pairings, and Ribbon Graphs

Anas A. Rahman, Daniel Munoz George, James A. Mingo

We elucidate a bijection between ribbon graphs on the real projective plane and non-crossing annular pairings that relate to the $1/ N$ correction term of the GOE and LOE spectral m…

math.OA2025

Second order free cumulants: product, commutator, and anti-commutator

Daniel Munoz George, Daniel Perales

Given two second order free random variables $a$ and $b$ , we study the second order free cumulants of their product $ab$ , their commutator $ab - ba$ , and their anti-commutator $ab+ba…

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 $lim_{N \to \infty} N^{r - 2} k_{r} (T r (X_{N}^{m_{1}}), \dots, T r (X_{N}^{m_{r}}))$ …