An exact formula for general spectral correlation function of random Hermitian matrices
Mathematical Physics
2008-11-26 v4 Condensed Matter
High Energy Physics - Theory
math.MP
Exactly Solvable and Integrable Systems
Abstract
We have found an exact formula expressing a general correlation function containing both products and ratios of characteristic polynomials of random Hermitian matrices. The answer is given in the form of a determinant. An essential difference from the previously studied correlation functions (of products only) is the appearance of non-polynomial functions along with the orthogonal polynomials. These non-polynomial functions are the Cauchy transforms of the orthogonal polynomials. The result is valid for any ensemble of beta=2 symmetry class and generalizes recent asymptotic formulae obtained for GUE and its chiral counterpart by different methods..
Cite
@article{arxiv.math-ph/0204051,
title = {An exact formula for general spectral correlation function of random Hermitian matrices},
author = {Yan V. Fyodorov and Eugene Strahov},
journal= {arXiv preprint arXiv:math-ph/0204051},
year = {2008}
}
Comments
published version, with a few misprints corrected