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- W2023372954 abstract "We consider the 2-dimensional Toda lattice tau functions τn(t,s;η,θ) deforming the probabilities τn(η,θ) that a randomly chosen matrix from the unitary group U(n), for the Haar measure, has no eigenvalues within an arc (η,θ) of the unit circle. We show that these tau functions satisfy a centerless Virasoro algebra of constraints, with a boundary part in the sense of Adler, Shiota and van Moerbeke. As an application, we obtain a new derivation of a differential equation due to Tracy and Widom, satisfied by these probabilities, linking it to the Painlevé VI equation." @default.
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- W2023372954 date "2011-08-01" @default.
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- W2023372954 title "A centerless representation of the Virasoro algebra associated with the unitary circular ensemble" @default.
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- W2023372954 doi "https://doi.org/10.1016/j.cam.2010.06.006" @default.
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