Limit shapes for growing extreme characters of U(∞)

Alexei Borodin, Alexey Bufetov, Grigori Olshanski

Research output: Contribution to journalArticlepeer-review

12 Citations (Scopus)


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.

Original languageEnglish
Pages (from-to)2339-2381
Number of pages43
JournalAnnals of Applied Probability
Issue number4
Publication statusPublished - 1 Aug 2015
Externally publishedYes


  • Extreme character
  • Limit shape
  • Signature


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