The Stable Random Matrix ensembles

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dc.creatorTierz, M.
dc.date2001-06-23
dc.date2003-04-26
dc.date.accessioned2026-07-07T02:41:53Z
dc.date.available2026-07-07T02:41:53Z
dc.descriptionWe address the construction of stable random matrix ensembles as the generalization of the stable random variables (Levy distributions). With a simple method we derive the Cauchy case, which is known to have remarkable properties. These properties allow for such an intuitive method -that relies on taking traces- to hold. Approximate but general results regarding the other distributions are derived as well. Some of the special properties of these ensembles are evidenced by showing partial failure of mean-field approaches. To conclude, we compute the confining potential that gives a Gaussian density of states in the limit of large matrices. The result is an hypergeometric function, in contrast with the simplicity of the Cauchy case.
dc.description17 pages. Stylistic changes. E-mail: tierz@ieec.fcr.es
dc.identifierhttps://arxiv.org/abs/cond-mat/0106485
dc.identifierhttp://arxiv.org/abs/cond-mat/0106485
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/17922
dc.subjectStatistical Mechanics
dc.subjectHigh Energy Physics - Theory
dc.subjectChaotic Dynamics
dc.titleThe Stable Random Matrix ensembles
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