RT Journal Article
T1 Partition functions and the continuum limit in Penner matrix models
A1 Álvarez Galindo, Gabriel
A1 Martínez Alonso, Luis
A1 Medina, helena
AB We present an implementation of the method of  orthogonal polynomials which is particularly suitable to study the partition functions of Penner random matrix models, to obtain their explicit forms in the exactly solvable cases, and to determine the coefficients of their perturbative expansions in the continuum limit. The method relies on identities satisfied by the resolvent of the Jacobi matrix in the three-term recursion relation of the associated families of orthogonal polynomials. These identities lead to a convenient formulation of the string equations. As an application, we show that in the continuum limit the free energy of certain exactly solvable models like the linear and double Penner models can be written as a sum of Gaussian contributions plus linear terms. To illustrate the one-cut case we discuss the linear, double and cubic Penner models, and for the two- cut case we discuss theoretically and numerically  the existence of a double-branch structure of the free energy for the Gaussian Penner model.
PB IOP Publishing Ltd
SN 1751-8113
YR 2014
FD 2014-08-08
LK https://hdl.handle.net/20.500.14352/34935
UL https://hdl.handle.net/20.500.14352/34935
LA eng
NO ©IOP Publishing Ltd.The financial support of the Ministerio de Ciencia e Innovación under project  IS2011-22566 is gratefully acknowledged
NO Ministerio de Ciencia e Innovación (MICINN)
DS Docta Complutense
RD 29 jun 2025