Gaussian multiplicative chaos for Gaussian Orthogonal and Symplectic Ensembles
Gaussian multiplicative chaos for Gaussian Orthogonal and Symplectic Ensembles
We study the characteristic polynomials of both the Gaussian Orthogonal and Symplectic Ensembles. We show that for both ensembles, powers of the absolute value of the characteristic polynomials converge in law to Gaussian multiplicative chaos measures after normalization for sufficiently small real powers. The main tool is a new asymptotic …