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Universality of Random Matrix Dynamics

descriptionPublicationkeyboard_double_arrow_right Article , Preprint 01 Jan 2020Embargo end date: 01 Jan 2020Publisher:Jagiellonian UniversityJournal:Acta Physica Polonica B, volume 51, page 1,641 (issn: 0587-4254, eissn: 1509-5770, Copyright policy )
Authors: Zdzislaw Burda;

doi: 10.5506/aphyspolb.51.1641 , 10.48550/arxiv.2005.09286

arXiv: http://arxiv.org/abs/2005.09286

Universality of Random Matrix Dynamics

Abstract

We discuss the concept of width-to-spacing ratio which plays the central role in the description of local spectral statistics of evolution operators in multiplicative and additive stochastic processes for random matrices. We show that the local spectral properties are highly universal and depend on a single parameter being the width-to-spacing ratio. We discuss duality between the kernel for Dysonian Brownian motion and the kernel for the Lyapunov matrix for the product of Ginibre matrices.

15 pages, 3 figures

Related Organizations
Keywords

Soft Condensed Matter (cond-mat.soft), FOS: Physical sciences, Mathematical Physics (math-ph), Condensed Matter - Soft Condensed Matter, Mathematical Physics

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citations
This is an alternative to the "Influence" indicator, which also reflects the overall/total impact of an article in the research community at large, based on the underlying citation network (diachronically).
BIP!Citations provided by BIP!
popularity
This indicator reflects the "current" impact/attention (the "hype") of an article in the research community at large, based on the underlying citation network.
BIP!Popularity provided by BIP!
influence
This indicator reflects the overall/total impact of an article in the research community at large, based on the underlying citation network (diachronically).
BIP!Influence provided by BIP!
impulse
This indicator reflects the initial momentum of an article directly after its publication, based on the underlying citation network.
BIP!Impulse provided by BIP!
1
Average
Average
Average
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gold