Dyson's constant for the hypergeometric kernel

Details Dyson's constant for the hypergeometric kernel Dyson's constant for the hypergeometric kernel

2009-10-10

arxiv.org/abs/0910.1914v2

Proc. of the Infinite Analysis 09, World Scientific, 2011, pp. 243-267

Physics

Mathematical Physics

17 pages, 2 figures; v2: added references and derivation of Painleve VI from Tracy-Widom equations

Scientific paper

We study a Fredholm determinant of the hypergeometric kernel arising in the representation theory of the infinite-dimensional unitary group. It is shown that this determinant coincides with the Palmer-Beatty-Tracy tau function of a Dirac operator on the hyperbolic disk. Solution of the connection problem for Painleve VI equation allows to determine its asymptotic behavior up to a constant factor, for which a conjectural expression is given in terms of Barnes functions. We also present analogous asymptotic results for the Whittaker and Macdonald kernel.

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