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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. doi:10.1016/j.aim.2008.06.012.

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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.

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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
Record Number:CaltechAUTHORS:BORaim08
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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, (
Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:13540
Deposited By: Tony Diaz
Deposited On:08 May 2009 17:16
Last Modified:08 Nov 2021 22:38

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