LIMIT SHAPES FOR GROWING EXTREME CHARACTERS OF U(∞)

被引：13

作者：

Borodin, Alexei ^{[1
,2
]}

Bufetov, Alexey ^{[2
,3
]}

Olshanski, Grigori ^{[2
,3
]}

机构：

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

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

[3] Higher Sch Econ, Moscow, Russia

来源：

ANNALS OF APPLIED PROBABILITY | 2015年 / 25卷 / 04期

基金：

美国国家科学基金会;

关键词：

Limit shape; extreme character; signature; DIMENSIONAL UNITARY-GROUP; PLANCHEREL MEASURE; SYMMETRICAL GROUP; YOUNG-DIAGRAMS; REPRESENTATIONS; ASYMPTOTICS;

D O I：

10.1214/14-AAP1050

中图分类号：

O21 [概率论与数理统计]; C8 [统计学];

学科分类号：

020208 ; 070103 ; 0714 ;

摘要：

We prove the existence of a limit shape and give its explicit description for certain probability distribution on signatures (or highest weights for unitary groups). The distributions have representation theoretic origin-they encode decomposition on irreducible characters of the restrictions of certain extreme characters of the infinite-dimensional unitary group U (infinity) to growing finite-dimensional unitary subgroups U (N). The characters of U(infinity) are allowed to depend on N. In a special case, this describes the hydrodynamic behavior for a family of random growth models in (2 + 1)-dimensions with varied initial conditions.

引用

页码：2339 / 2381

页数：43

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