Limit shapes for growing extreme characters of U(∞)
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Borodin_Limit shapes for growing.pdf
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Author(s)
Borodin, Alexei
Bufetov, Alexey
Olshanski, Grigori
Date Issued
August 2015
Journal
Annals of Applied Probability
Publisher
Institute of Mathematical Statistics
Citation
Borodin, Alexei, Alexey Bufetov, and Grigori Olshanski. “Limit Shapes for Growing Extreme Characters of $U(\infty)$.” The Annals of Applied Probability 25, no. 4 (August 2015): 2339–2381. doi:10.1214/14-aap1050. © 2015 Institute of Mathematical Statistics
Version
Author's final manuscript
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(∞) 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.
MIT Department
Massachusetts Institute of Technology. Department of Mathematics
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Creative Commons Attribution-Noncommercial-Share Alike
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DOI of Published Version
https://doi.org/10.1214/14-aap1050
