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Álvarez Galindo, Gabriel ; Martínez Alonso, Luis ; Medina Reus, Elena | Elsevier Science BV | 2011-07-11We present a method to compute the genus expansion of the free energy of Hermitian matrix models from the large N expansion of the recurrence coefficients of the associated family of orthogonal polynomials. The method is based on the Bleher-Its [...]texto impreso
In this work we use Riemann-Hilbert problems for multiple orthogonal polynomials in order to derive string equations associated to Lax-Orlov pairs operators. These string equations provide us with a useful tool to analyze the large n-limit of th[...]texto impreso
A previously introduced scheme for describing integrable deformations of algebraic curves is completed. Lenard relations are used to characterize and classify these deformations in terms of hydrodynamic-type systems. A general solution of the co[...]texto impreso
It is proved that the system of string equations of the dispersionless 2-Toda hierarchy which arises in the planar limit of the hermitian matrix model also underlies certain processes in HeleShaw flows.texto impreso
Álvarez Galindo, Gabriel ; Martínez Alonso, Luis ; Medina Reus, Elena | 2013-06This paper deals with the determination of the S-curves in the theory of non-hermitian orthogonal polynomials with respect to exponential weights along suitable paths in the complex plane. It is known that the corresponding complex equilibrium p[...]texto impreso
A class of exact solutions of the dispersionless Toda hierarchy constrained by a string equation is obtained. These solutions represent deformations of analytic curves with a finite number of nonzero harmonic moments. The corresponding tau-funct[...]texto impreso
Wide classes of explicit solutions of the Manin-Radul and Jacobian supersymmetric KP hierarchies are constructed by using line bundles over complex supercurves based on the Riemann sphere. Their construction extends several ideas of the standard[...]texto impreso
Álvarez, Gabriel ; Martínez Alonso, Luis ; Medina Reus, Elena | Academic Press Inc Elsevier Science | 2015-10In 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 produ[...]texto impreso
We consider the following system: [GRAPHICS] which has been used as a model for various phenomena, including motion of species by chemotaxis and equilibrium of self-attracting clusters. We show that, in space dimension N = 3, (S) possess radial [...]texto impreso
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A scheme for solving quasiclassical-string equations is developed to prove that genus-zero hitham hierarchies describe the deformations of planar domains determined by rational conformal-maps. This property is applied in normal matrix models to[...]texto impreso
We propose to use eigenvalue densities of unitary random matrix ensembles as mass distributions in gravitational lensing. The corresponding lens equations reduce to algebraic equations in the complex plane which can be treated analytically. We p[...]texto impreso
Kodama, Y. ; Konopelchenko, Boris ; Martínez Alonso, Luis ; Medina Reus, Elena | American Institute of Physics | 2005-11A general scheme for determining and studying hydrodynamic type systems describing integrable deformations of algebraic curves is applied to cubic curves. Lagrange resolvents of the theory of cubic equations are used to derive and characterize t[...]texto impreso
Single-field inflaton models in the kinetic dominance period admit formal solutions given by generalized asymptotic expansions called psi series. We present a method for computing psi series for the Hubble parameter as a function of the inflaton[...]texto impreso
Álvarez Galindo, Gabriel ; Martínez Alonso, Luis ; Medina Reus, Elena | IOP publishing ltd | 2011-07-15We present a method to characterize and compute the large N formal asymptotics of regular and critical Hermitian matrix models with general even potentials in the one-cut and two-cut cases. Our analysis is based on a method to solve continuum li[...]
