Fluctuations of particle systems determined by Schur generating functions

被引：29

作者：

Bufetov, Alexey ^{[1
]}

Gorin, Vadim ^{[1
,2
]}

机构：

[1] MIT, Dept Math, Cambridge, MA 02139 USA

[2] Russian Acad Sci, Inst Informat Transmiss Problems, Moscow, Russia

来源：

ADVANCES IN MATHEMATICS | 2018年 / 338卷

关键词：

Schur functions; Asymptotic representation theory; Random tilings; GAUSSIAN FREE FIELDS; 2ND-ORDER FREENESS; PLANCHEREL MEASURE; RANDOM MATRICES; RANDOM SURFACES; YOUNG-DIAGRAMS; ASYMPTOTICS; REPRESENTATIONS; U(INFINITY); CHARACTERS;

D O I：

10.1016/j.aim.2018.07.009

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

We develop a new toolbox for the analysis of the global behavior of stochastic discrete particle systems. We introduce and study the notion of the Schur generating function of a random discrete configuration. Our main result provides a Central Limit Theorem (CLT) for such a configuration given certain conditions on the Schur generating function. As applications of this approach, we prove CLT's for several probabilistic models coming from asymptotic representation theory and statistical physics, including random lozenge and domino Wings, non-intersecting random walks, decompositions of tensor products of representations of unitary groups. (C) 2018 Elsevier Inc. All rights reserved.

引用

页码：702 / 781

页数：80

共 60 条

[51] Conditioned random walks and the RSK correspondence [J].