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Regular version of the site

Article

Limit shapes for growing extreme characters of U(∞)

Annals of Applied Probability. 2015. Vol. 25. No. 4. P. 2339-2381.
Borodin A., Bufetov A., Olshanski G.

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(∞) to growing finite-dimensional unitary subgroups U(N). The characters of U(∞) 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. © Institute of Mathematical Statistics, 2015.