Interacting particle systems at the edge of multilevel Dyson Brownian motions

Vadim Gorin; Mykhaylo Shkolnikov

doi:10.1016/j.aim.2016.08.034

Interacting particle systems at the edge of multilevel Dyson Brownian motions

Vadim Gorin, Mykhaylo Shkolnikov

Research output: Contribution to journal › Article › peer-review

4 Scopus citations

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.

Original language	English (US)
Pages (from-to)	90-130
Number of pages	41
Journal	Advances in Mathematics
Volume	304
DOIs	https://doi.org/10.1016/j.aim.2016.08.034
State	Published - Jan 2 2017

All Science Journal Classification (ASJC) codes

General Mathematics

Keywords

Beta random matrix models
Dyson Brownian motions
Interacting particle systems with local interactions
Minors of random matrices
Singular stochastic differential equations

Access to Document

10.1016/j.aim.2016.08.034

Cite this

@article{29478a30f07b4ee99ea459a9f2399784,

title = "Interacting particle systems at the edge of multilevel Dyson Brownian motions",

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",

author = "Vadim Gorin and Mykhaylo Shkolnikov",

note = "Publisher Copyright: {\textcopyright} 2016 Elsevier Inc.",

year = "2017",

month = jan,

day = "2",

doi = "10.1016/j.aim.2016.08.034",

language = "English (US)",

volume = "304",

pages = "90--130",

journal = "Advances in Mathematics",

issn = "0001-8708",

publisher = "Academic Press Inc.",

}

TY - JOUR

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

AU - Gorin, Vadim

AU - Shkolnikov, Mykhaylo

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

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

U2 - 10.1016/j.aim.2016.08.034

DO - 10.1016/j.aim.2016.08.034

M3 - Article

AN - SCOPUS:84986898432

SN - 0001-8708

VL - 304

SP - 90

EP - 130

JO - Advances in Mathematics

JF - Advances in Mathematics

ER -

Interacting particle systems at the edge of multilevel Dyson Brownian motions

Abstract

All Science Journal Classification (ASJC) codes

Keywords

Access to Document

Other files and links

Fingerprint

Cite this