# Exact and explicit evaluation of Brezin-Hikami kernels

Source: [Exact and explicit evaluation of Brezin-Hikami kernels](<https://www.sota2.com/research/paper/68fa30981e209131ce876a60>)

Collection index: [llms.txt](<https://www.sota2.com/research/llms.txt>)

Data updated: 2025-10-24T18:18:05.084Z

Authors: K. Gorska, K. A. Penson

Published: 2012-11-19T16:02:41.000Z

## 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.

## Recorded benchmark results

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## Original sources and implementation

[Original paper](<https://arxiv.org/abs/1211.4478>)

[PDF](<https://arxiv.org/pdf/1211.4478.pdf>)