TY - JOUR

T1 - Interacting particle systems at the edge of multilevel Dyson Brownian motions

AU - Gorin, Vadim

AU - Shkolnikov, Mykhaylo

N1 - Funding Information:
We would like to thank Alexei Borodin, Paul Bourgade, Amir Dembo, Alice Guionnet, Sasha Sodin and Ofer Zeitouni for many fruitful discussions. In particular, we thank Alice Guionnet and Ofer Zeitouni for showing us the integration by parts trick employed in the proof of Lemma 3.7 . V.G. was partially supported by the NSF grant DMS-1407562 and M.S. was partially supported by the NSF grant DMS-1506290.

PY - 2017/1/2

Y1 - 2017/1/2

N2 - 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.

AB - 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.

KW - Beta random matrix models

KW - Dyson Brownian motions

KW - Interacting particle systems with local interactions

KW - Minors of random matrices

KW - Singular stochastic differential equations

UR - http://www.scopus.com/inward/record.url?scp=84986898432&partnerID=8YFLogxK

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U2 - 10.1016/j.aim.2016.08.034

DO - 10.1016/j.aim.2016.08.034

M3 - Article

AN - SCOPUS:84986898432

VL - 304

SP - 90

EP - 130

JO - Advances in Mathematics

JF - Advances in Mathematics

SN - 0001-8708

ER -