0 O ct 2 00 1 ASYMPTOTIC REPRESENTATION THEORY AND RIEMANN – HILBERT PROBLEM
نویسنده
چکیده
We show how the Riemann–Hilbert problem can be used to compute correlation kernels for determinantal point processes arising in different models of asymptotic combinatorics and representation theory. The Whittaker kernel and the discrete Bessel kernel are computed as examples.
منابع مشابه
ar X iv : m at h - ph / 0 11 10 07 v 1 5 N ov 2 00 1 FREDHOLM DETERMINANTS , JIMBO - MIWA - UENO TAU - FUNCTIONS , AND REPRESENTATION THEORY
The authors show that a wide class of Fredholm determinants arising in the representation theory of " big " groups such as the infinite–dimensional unitary group, solve Painlevé equations. Their methods are based on the theory of integrable operators and the theory of Riemann–Hilbert problems.
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