Discrete Painlev equations and random matrix averages
نویسندگان
چکیده
منابع مشابه
Discrete Painlevé Equations and Random Matrix Averages
The τ-function theory of Painlevé systems is used to derive recurrences in the rank n of certain random matrix averages over U (n). These recurrences involve auxilary quantities which satisfy discrete Painlevé equations. The random matrix averages include cases which can be interpreted as eigenvalue distributions at the hard edge and in the bulk of matrix ensembles with unitary symmetry. The re...
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In this paper we study surfaces immersed in R such that the mean curvature function H satisfies the equation (1=H) = 0, where is the Laplace operator of the induced metric. We call them HIMC surfaces. All HIMC surfaces of revolution are classified in terms of the third Painlevé transcendent. In the general class of HIMC surfaces we distinguish a subclass of -isothermic surfaces, which is a gene...
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ژورنال
عنوان ژورنال: Nonlinearity
سال: 2003
ISSN: 0951-7715,1361-6544
DOI: 10.1088/0951-7715/16/6/303