Asymptotics of Plancherel measures for the infinite-dimensional unitary group

• Autores: Alexei Borodin, Jeffrey Kuan
• Localización: Advances in mathematics, ISSN 0001-8708, Vol. 219, Nº 3, 2008, págs. 894-931
• Idioma: inglés
• DOI: 10.1016/j.aim.2008.06.012
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• Resumen

  • 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+xZ, 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.