Complex Wishart Ensemble and KP τ Functions
نویسنده
چکیده
where S is an n × n positive definite Hermitian matrix, dS is equivalent to the dH in (1) restricted in the subset of positive definite Hermitian matrices, and E+ is a subset of R+. The integral H(E) is in some sense the limiting case of L(E+), since H(E) can be evaluated by Hermitian polynomials, while L(E+) by Laguerre polynomials in the same way [8]. It is a classical result that Hermitian polynomials are the limits of Laguerre polynomials after shifting and rescaling [18]. The GUE has a natural generalization by adding parameters. Let p1, . . . , p2m be arbitrary real numbers, with p2m < 0, then we define M(E; p1, . . . , p2m) = ∫
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