Interacting particle systems at the edge of multilevel Dyson Brownian motions
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Gorin_nteracting particle systems.pdf
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Author(s)
Gorin, Vadim
Shkolnikov, Mykhaylo
Date Issued
September 2016
Journal
Advances in Mathematics
Publisher
Elsevier BV
Citation
Gorin, Vadim, and Mykhaylo Shkolnikov. “Interacting Particle Systems at the Edge of Multilevel Dyson Brownian Motions.” Advances in Mathematics 304 (January 2017): 90–130 © 2016 Elsevier Inc
Version
Original manuscript
Abstract
We study the joint asymptotic behavior of spacings between particles at the edge of multilevel Dyson Brownian motions, when the number of levels tends to infinity. Despite the global interactions between particles in multilevel Dyson Brownian motions, we observe a decoupling phenomenon in the limit: the global interactions become negligible and only the local interactions remain. The resulting limiting objects are interacting particle systems which can be described as Brownian versions of certain totally asymmetric exclusion processes. This is the first appearance of a particle system with local interactions in the context of general β random matrix models. Keywords: Beta random matrix models; Dyson Brownian motions; Interacting particle systems with local interactions; Minors of random matrices; Singular stochastic differential equations
MIT Department
Massachusetts Institute of Technology. Department of Mathematics
Terms of Use
Creative Commons Attribution-NonCommercial-NoDerivs License
Persistent DSpace Link
DOI of Published Version
https://doi.org/10.1016/j.aim.2016.08.034
