Free Random Levy Matrices

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dc.creatorBurda, Z.
dc.creatorJanik, R. A.
dc.creatorJurkiewicz, J.
dc.creatorNowak, M. A.
dc.creatorPapp, G.
dc.creatorZahed, I.
dc.date2000-11-27
dc.date.accessioned2026-07-07T02:39:35Z
dc.date.available2026-07-07T02:39:35Z
dc.descriptionUsing the theory of free random variables (FRV) and the Coulomb gas analogy, we construct stable random matrix ensembles that are random matrix generalizations of the classical one-dimensional stable Lévy distributions. We show that the resolvents for the corresponding matrices obey transcendental equations in the large size limit. We solve these equations in a number of cases, and show that the eigenvalue distributions exhibit Lévy tails. For the analytically known Lévy measures we explicitly construct the density of states using the method of orthogonal polynomials. We show that the Lévy tail-distributions are characterized by a novel form of microscopic universality.
dc.description5 pages
dc.identifierhttps://arxiv.org/abs/cond-mat/0011451
dc.identifierhttp://arxiv.org/abs/cond-mat/0011451
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/17063
dc.subjectMesoscale and Nanoscale Physics
dc.titleFree Random Levy Matrices
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