# Compact support probability distributions in random matrix theory

Akemann G, Cicuta GM, Molinari L, Vernizzi G (1999)
Phys.Rev.E 59(2): 1489-1497.

Journal Article | Published | English

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Abstract
We consider a generalization of the fixed and bounded trace ensemblesintroduced by Bronk and Rosenzweig up to an arbitrary polynomial potential. Inthe large-N limit we prove that the two are equivalent and that theireigenvalue distribution coincides with that of the "canonical" ensemble withmeasure exp[-$n$Tr V(M)]. The mapping of the corresponding phase boundaries isilluminated in an explicit example. In the case of a Gaussian potential we areable to derive exact expressions for the one- and two-point correlator forfinite $n$, having finite support.
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Akemann G, Cicuta GM, Molinari L, Vernizzi G. Compact support probability distributions in random matrix theory. Phys.Rev.E. 1999;59(2):1489-1497.
Akemann, G., Cicuta, G. M., Molinari, L., & Vernizzi, G. (1999). Compact support probability distributions in random matrix theory. Phys.Rev.E, 59(2), 1489-1497.
Akemann, G., Cicuta, G. M., Molinari, L., and Vernizzi, G. (1999). Compact support probability distributions in random matrix theory. Phys.Rev.E 59, 1489-1497.
Akemann, G., et al., 1999. Compact support probability distributions in random matrix theory. Phys.Rev.E, 59(2), p 1489-1497.
G. Akemann, et al., “Compact support probability distributions in random matrix theory”, Phys.Rev.E, vol. 59, 1999, pp. 1489-1497.
Akemann, G., Cicuta, G.M., Molinari, L., Vernizzi, G.: Compact support probability distributions in random matrix theory. Phys.Rev.E. 59, 1489-1497 (1999).
Akemann, Gernot, Cicuta, G. M., Molinari, L., and Vernizzi, G. “Compact support probability distributions in random matrix theory”. Phys.Rev.E 59.2 (1999): 1489-1497.
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arXiv cond-mat/9809270