Compact support probability distributions in random matrix theory

Details Compact support probability distributions in random matrix theory Compact support probability distributions in random matrix theory

1998-09-21

arxiv.org/abs/cond-mat/9809270v1

Phys.Rev.E 59 (1999) 1489-1497.

Physics

Condensed Matter

LaTeX, 14 pages+title page

Scientific paper

10.1103/PhysRevE.59.1489

We consider a generalization of the fixed and bounded trace ensembles introduced by Bronk and Rosenzweig up to an arbitrary polynomial potential. In the large-N limit we prove that the two are equivalent and that their eigenvalue distribution coincides with that of the "canonical" ensemble with measure exp[-$n$Tr V(M)]. The mapping of the corresponding phase boundaries is illuminated in an explicit example. In the case of a Gaussian potential we are able to derive exact expressions for the one- and two-point correlator for finite $n$, having finite support.

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