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http://bura.brunel.ac.uk/handle/2438/499
Title: | Compact support probability distributions in random matrix theory |
Authors: | Akemann, G Cicuta, GM Molinari, L Vernizzi, G |
Issue Date: | 1998 |
Publisher: | American Physical Society |
Citation: | Physical Review E, 59(2): 1489 - 1497, Feb 1999 |
Abstract: | 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. |
URI: | http://bura.brunel.ac.uk/handle/2438/499 |
DOI: | http://dx.doi.org/10.1103/PhysRevE.59.1489 |
Appears in Collections: | Publications Dept of Mathematics Research Papers Mathematical Sciences |
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