Fluctuation formula for complex random matrices
统计力学
2007-05-23 v1
摘要
A Gaussian fluctuation formula is proved for linear statistics of complex random matrices in the case that the statistic is rotationally invariant. For a general linear statistic without this symmetry, Coulomb gas theory is used to predict that the distribution will again be a Gaussian, with a specific mean and variance. The variance splits naturally into a bulk and surface contibution, the latter resulting from the long range correlations at the boundary of the support of the eigenvalue density.
引用
@article{arxiv.cond-mat/9805306,
title = {Fluctuation formula for complex random matrices},
author = {P. J. Forrester},
journal= {arXiv preprint arXiv:cond-mat/9805306},
year = {2007}
}
备注
5 pages