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

Alexei Borodin; Alexey Bufetov; Grigori Olshanski

doi:10.1214/14-aap1050

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arXiv · 1311.5697

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

Alexei Borodin·Alexey Bufetov·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.

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BibTeX RIS

Alexei Borodin, Alexey Bufetov, Grigori Olshanski. 2015-06-29. Limit shapes for growing extreme characters of $U(\infty)$. https://doi.org/10.1214/14-aap1050

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