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arXiv · 1211.4478

Exact and explicit evaluation of Brezin-Hikami kernels

K. Gorska·K. A. Penson
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Abstract

We present exact and explicit form of the kernels $hat{K}(x, y)$ 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 $hat{K}(x, y)$'s.

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BibTeXRIS

K. Gorska, K. A. Penson. 2013-04-20. Exact and explicit evaluation of Brezin-Hikami kernels. https://doi.org/10.1016/j.nuclphysb.2013.04.005

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