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.
Funding Statement
The author was partially supported by the grants NSF DMS-165355 and NSF DMS-1502632 during the completion of this work.
Citation
Pax Kivimae. "Gaussian multiplicative chaos for Gaussian Orthogonal and Symplectic Ensembles." Electron. J. Probab. 29 1 - 71, 2024. https://doi.org/10.1214/24-EJP1083
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