The Annals of Applied Probability

Limit shapes for growing extreme characters of $U(\infty)$

Alexei Borodin, Alexey Bufetov, and Grigori Olshanski

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Abstract

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 $U(\infty)$ to growing finite-dimensional unitary subgroups $U(N)$. The characters of $U(\infty)$ 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.

Article information

Source
Ann. Appl. Probab., Volume 25, Number 4 (2015), 2339-2381.

Dates
Received: December 2013
Revised: June 2014
First available in Project Euclid: 21 May 2015

Permanent link to this document
https://projecteuclid.org/euclid.aoap/1432212444

Digital Object Identifier
doi:10.1214/14-AAP1050

Mathematical Reviews number (MathSciNet)
MR3349009

Zentralblatt MATH identifier
1325.60013

Subjects
Primary: 60F05: Central limit and other weak theorems
Secondary: 22E66: Analysis on and representations of infinite-dimensional Lie groups

Keywords
Limit shape extreme character signature

Citation

Borodin, Alexei; Bufetov, Alexey; Olshanski, Grigori. Limit shapes for growing extreme characters of $U(\infty)$. Ann. Appl. Probab. 25 (2015), no. 4, 2339--2381. doi:10.1214/14-AAP1050. https://projecteuclid.org/euclid.aoap/1432212444


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