Universality for Multiplicative Statistics of Hermitian Random Matrices and the Integro-Differential Painlevé II Equation
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220_2022_Article_4518.pdf
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1.05 MB
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Author(s)
Ghosal, Promit
Silva, Guilherme L. F.
Date Issued
November 10, 2022
Publisher
Springer Berlin Heidelberg
Citation
Ghosal, Promit and Silva, Guilherme L. F. 2022. "Universality for Multiplicative Statistics of Hermitian Random Matrices and the Integro-Differential Painlevé II Equation."
Version
Final published version
Abstract
Abstract
We study multiplicative statistics for the eigenvalues of unitarily-invariant Hermitian random matrix models. We consider one-cut regular polynomial potentials and a large class of multiplicative statistics. We show that in the large matrix limit several associated quantities converge to limits which are universal in both the polynomial potential and the family of multiplicative statistics considered. In turn, such universal limits are described by the integro-differential Painlevé II equation, and in particular they connect the random matrix models considered with the narrow wedge solution to the KPZ equation at any finite time.
MIT Department
Massachusetts Institute of Technology. Department of Mathematics
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DOI of Published Version
https://doi.org/10.1007/s00220-022-04518-3
