Exact and explicit evaluation of Brezin-Hikami kernels

Abstract

We present exact and explicit form of the kernels $hatK(x,y)$ appearing in the theory of energy correlations in the ensembles of Hermitian random matrices with Gaussian probability distribution, see E. Brezin and S. Hikami, Phys. Rev. E 57, 4140 and E 58, 7176 (1998). In obtaining this result we have exploited the analogy with the method of producing exact forms of two-sided, symmetric Levy stable laws, presented by us recently. This result is valid for arbitrary values of parameters in question. We furnish analytical and graphical representations of physical quantities calculated from $hatK(x,y)$'s.

Improved presentation: two new figures added, two new appendices added

References in corpus (4)

• Exact and explicit probability densities for one-sided Levy stable distributions
• Levy stable two-sided distributions: exact and explicit densities for asymmetric case
• Levy stable distributions via associated integral transform
• Operator solutions for fractional Fokker-Planck equations

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• An Algebraic Approach to Fourier Transformation