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Título:
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Fine structure in the large n limit of the non-hermitian Penner matrix model
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Autores:
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Álvarez, Gabriel ;
Martínez Alonso, Luis ;
Medina Reus, Elena
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Tipo de documento:
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texto impreso
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Editorial:
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Academic Press Inc Elsevier Science, 2015-10
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Dimensiones:
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application/pdf
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Nota general:
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info:eu-repo/semantics/openAccess
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Idiomas:
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Palabras clave:
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Estado = Publicado
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Materia = Ciencias: Física: Física-Modelos matemáticos
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Materia = Ciencias: Física: Física matemática
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Tipo = Artículo
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Resumen:
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In this paper we apply results on the asymptotic zero distribution of the Laguerre polynomials to discuss generalizations of the standard large n limit in the non-hermitian Penner matrix model. In these generalizations g_(n)n ? t, but the product g_(n)n is not necessarily fixed to the value of the ’t Hooft coupling t. If t > 1 and the limit l = lim_(n??) |sin(?/g_n)| ^(1/n) exists, then the large n limit is well-defined but depends both on t and on l. This result implies that for t > 1 the standard large n limit with g_(n)n = t fixed is not well-defined. The parameter l determines a fine structure of the asymptotic eigenvalue support: for l ? 0 the support consists of an interval on the real axis with charge fraction Q = 1 ? 1/t and an l-dependent oval around the origin with charge fraction 1/t. For l = 1 these two components meet, and for l = 0 the oval collapses to the origin. We also calculate the total electrostatic energy ? which turns out to be independent of l, and the free energy ? = ? - ? ln l, which does depend of the fine structure parameter l. The existence of large n asymptotic expansions of ? beyond the planar limit as well as the double-scaling limit are also discussed.
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En línea:
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https://eprints.ucm.es/33245/1/alvarez13preprint.pdf
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