Borodin, Alexei and Kuan, Jeffrey (2008) Asymptotics of Plancherel measures for the infinite-dimensional unitary group. Advances in Mathematics, 219 (3). pp. 894-931. ISSN 0001-8708. doi:10.1016/j.aim.2008.06.012. https://resolver.caltech.edu/CaltechAUTHORS:BORaim08
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Abstract
We study a two-dimensional family of probability measures on infinite Gelfand-Tsetlin schemes induced by a distinguished family of extreme characters of the infinite-dimensional unitary group. These measures are unitary group analogs of the well-known Plancherel measures for symmetric groups. We show that any measure from our family defines a determinantal point process on Z_+ x Z, and we prove that in appropriate scaling limits, such processes converge to two different extensions of the discrete sine process as well as to the extended Airy and Pearcey processes.
| Item Type: | Article | |||||||||
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| Additional Information: | © 2008 Elsevier B.V. Received 8 January 2008; accepted 9 June 2008. Available online 18 July 2008. Communicated by the Managing Editors of AIM. The authors are very grateful to Grigori Olshanski for a number of valuable suggestions. We would also like to thank the referee for many helpful remarks. The first named author (A.B.) was partially supported by the NSF grant DMS-0707163. | |||||||||
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| Subject Keywords: | plancherel measures; infinite-dimensional unitary group; determinantal point processes | |||||||||
| Issue or Number: | 3 | |||||||||
| DOI: | 10.1016/j.aim.2008.06.012 | |||||||||
| Record Number: | CaltechAUTHORS:BORaim08 | |||||||||
| Persistent URL: | https://resolver.caltech.edu/CaltechAUTHORS:BORaim08 | |||||||||
| Official Citation: | Alexei Borodin, Jeffrey Kuan, Asymptotics of Plancherel measures for the infinite-dimensional unitary group, Advances in Mathematics, Volume 219, Issue 3, 2008, Pages 894-931, ISSN 0001-8708, https://doi.org/10.1016/j.aim.2008.06.012. (http://www.sciencedirect.com/science/article/pii/S000187080800159X) | |||||||||
| Usage Policy: | No commercial reproduction, distribution, display or performance rights in this work are provided. | |||||||||
| ID Code: | 13540 | |||||||||
| Collection: | CaltechAUTHORS | |||||||||
| Deposited By: | Tony Diaz | |||||||||
| Deposited On: | 08 May 2009 17:16 | |||||||||
| Last Modified: | 08 Nov 2021 22:38 |
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