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.
Publisher Copyright:
© 2016 Elsevier Inc.
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
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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
SN - 0001-8708
VL - 304
SP - 90
EP - 130
JO - Advances in Mathematics
JF - Advances in Mathematics
ER -