Dyson's constant for the hypergeometric kernel
Mathematical Physics
2011-03-25 v2 High Energy Physics - Theory
math.MP
Exactly Solvable and Integrable Systems
Abstract
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.
Cite
@article{arxiv.0910.1914,
title = {Dyson's constant for the hypergeometric kernel},
author = {O. Lisovyy},
journal= {arXiv preprint arXiv:0910.1914},
year = {2011}
}
Comments
17 pages, 2 figures; v2: added references and derivation of Painleve VI from Tracy-Widom equations