Limit shapes for growing extreme characters of U(∞)
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 cert...
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| Format: | Article |
| Language: | en_US |
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Institute of Mathematical Statistics
2017
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| Online Access: | http://hdl.handle.net/1721.1/110172 https://orcid.org/0000-0002-2913-5238 https://orcid.org/0000-0003-4019-8309 |
| _version_ | 1826209932276400128 |
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| author | Borodin, Alexei Bufetov, Alexey Olshanski, Grigori |
| author2 | Massachusetts Institute of Technology. Department of Mathematics |
| author_facet | Massachusetts Institute of Technology. Department of Mathematics Borodin, Alexei Bufetov, Alexey Olshanski, Grigori |
| author_sort | Borodin, Alexei |
| collection | MIT |
| description | 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. |
| first_indexed | 2024-09-23T14:36:08Z |
| format | Article |
| id | mit-1721.1/110172 |
| institution | Massachusetts Institute of Technology |
| language | en_US |
| last_indexed | 2024-09-23T14:36:08Z |
| publishDate | 2017 |
| publisher | Institute of Mathematical Statistics |
| record_format | dspace |
| spelling | mit-1721.1/1101722022-09-29T09:55:36Z Limit shapes for growing extreme characters of U(∞) Borodin, Alexei Bufetov, Alexey Olshanski, Grigori Massachusetts Institute of Technology. Department of Mathematics Borodin, Alexei Bufetov, Alexey 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. National Science Foundation (U.S.) (Grant DMS-10-56390) Simons Foundation (Simons Foundation-IUM scholarship) Moebius Foundation for Young Scientists Dynasty Foundation Russian Foundation for Basic Research 2017-06-22T18:06:19Z 2017-06-22T18:06:19Z 2015-08 2014-06 Article http://purl.org/eprint/type/JournalArticle 1050-5164 http://hdl.handle.net/1721.1/110172 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 https://orcid.org/0000-0002-2913-5238 https://orcid.org/0000-0003-4019-8309 en_US http://dx.doi.org/10.1214/14-aap1050 Annals of Applied Probability Creative Commons Attribution-Noncommercial-Share Alike http://creativecommons.org/licenses/by-nc-sa/4.0/ application/pdf Institute of Mathematical Statistics arXiv |
| spellingShingle | Borodin, Alexei Bufetov, Alexey Olshanski, Grigori Limit shapes for growing extreme characters of U(∞) |
| title | Limit shapes for growing extreme characters of U(∞) |
| title_full | Limit shapes for growing extreme characters of U(∞) |
| title_fullStr | Limit shapes for growing extreme characters of U(∞) |
| title_full_unstemmed | Limit shapes for growing extreme characters of U(∞) |
| title_short | Limit shapes for growing extreme characters of U(∞) |
| title_sort | limit shapes for growing extreme characters of u ∞ |
| url | http://hdl.handle.net/1721.1/110172 https://orcid.org/0000-0002-2913-5238 https://orcid.org/0000-0003-4019-8309 |
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