Gaussian Multiplicative Chaos for Gaussian Orthogonal and Symplectic Ensembles
Probability
2022-10-28 v4 Mathematical Physics
math.MP
Abstract
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 relation between the fractional moments of the absolute characteristic polynomials of Gaussian Orthogonal, Unitary, and Symplectic Ensembles.
Keywords
Cite
@article{arxiv.2012.09969,
title = {Gaussian Multiplicative Chaos for Gaussian Orthogonal and Symplectic Ensembles},
author = {Pax Kivimae},
journal= {arXiv preprint arXiv:2012.09969},
year = {2022}
}
Comments
73 pages. Version 3: Significant expansion of the proofs in Section 6 and Section 7. Corrections for many minor errors and typos