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Asymptotics of Plancherel measures for the infinite-dimensional unitary group

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. 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
Related URLs:
URLURL TypeDescription
http://dx.doi.org/10.1016/j.aim.2008.06.012DOIArticle
https://arxiv.org/abs/0712.1848arXivDiscussion Paper
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.
Funders:
Funding AgencyGrant Number
NSFDMS-0707163
Subject Keywords:plancherel measures; infinite-dimensional unitary group; determinantal point processes
Issue or Number:3
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:03 Oct 2019 00:39

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