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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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

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

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

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Zentralblatt MATH identifier

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

Limit shape extreme character signature


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.

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