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Published October 20, 2008 | Submitted
Journal Article Open

Asymptotics of Plancherel measures for the infinite-dimensional unitary group

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.

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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