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|Title:||Compact support probability distributions in random matrix theory|
|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.|
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Dept of Mathematics Research Papers
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