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

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.

Published at http://dx.doi.org/10.1214/14-AAP1050 in the Annals of Applied Probability (http://www.imstat.org/aap/) by the Institute of Mathematical Statistics (http://www.imstat.org)

References in corpus (1)

• Plancherel representations of $U(\infty )$ and correlated Gaussian Free Fields

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