3 papers
math.PR2026
Loop Equations Characterize Random Matrix Statistics
Paul Bourgade, Jiaoyang Huang
We prove that the universal local point processes of random matrix theory are characterized by their loop equation hierarchies. More precisely, for every rational , the $\mat…
math.PR2026
Fluctuations for non-Hermitian dynamics
Paul Bourgade, Giorgio Cipolloni, Jiaoyang Huang
We prove that under the Brownian evolution on large non-Hermitian matrices the log-determinant converges in distribution to a 2+1 dimensional Gaussian field in the Edwards-Wilkinso…
math.PR2026
Fisher-Hartwig asymptotics for non-Hermitian random matrices
Paul Bourgade, Guillaume Dubach, Lisa Hartung +1
We prove the two-dimensional analogue of the asymptotics for Toeplitz determinants with Fisher-Hartwig singularities, for general real symbols. This formula has applications to ran…