Asymptotics of Plancherel measures for the infinite-dimensional unitary group |
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Authors: | Alexei Borodin Jeffrey Kuan |
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Institution: | California Institute of Technology, Department of Mathematics 253-37, Pasadena, CA, United States |
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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+×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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Keywords: | Plancherel measures Infinite-dimensional unitary group Determinantal point processes |
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