# Asymptotics of the partition function of a random matrix model

Pavel M. Bleher^{[1]}; Alexander Its

- [1] Indiana University-Purdue University Indianapolis, department of mathematical sciences, 402 N. Blackford Street, Indianapolis IN 46202 (USA)

Annales de l’institut Fourier (2005)

- Volume: 55, Issue: 6, page 1943-2000
- ISSN: 0373-0956

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topM. Bleher, Pavel, and Its, Alexander. "Asymptotics of the partition function of a random matrix model." Annales de l’institut Fourier 55.6 (2005): 1943-2000. <http://eudml.org/doc/116239>.

@article{M2005,

abstract = {We prove a number of results concerning the large $N$ asymptotics of the free energy of a
random matrix model with a polynomial potential. Our approach is based on a deformation
of potential and on the use of the underlying integrable structures of the matrix model.
The main results include the existence of a full asymptotic expansion in even powers of
$N$ of the recurrence coefficients of the related orthogonal polynomials for a one-cut
regular potential and the double scaling asymptotics of the free energy for a singular
quartic potential. We also prove the analyticity of the coefficients of the asymptotic
expansions of the recurrence coefficients and the free energy, with respect to the
coefficients of the potential, and the one-sided analyticity of the recurrent
coefficients and the free energy for a one-cut singular potential.},

affiliation = {Indiana University-Purdue University Indianapolis, department of mathematical sciences, 402 N. Blackford Street, Indianapolis IN 46202 (USA)},

author = {M. Bleher, Pavel, Its, Alexander},

journal = {Annales de l’institut Fourier},

keywords = {Matrix Models; orthogonal polynomials; partition function},

language = {eng},

number = {6},

pages = {1943-2000},

publisher = {Association des Annales de l'Institut Fourier},

title = {Asymptotics of the partition function of a random matrix model},

url = {http://eudml.org/doc/116239},

volume = {55},

year = {2005},

}

TY - JOUR

AU - M. Bleher, Pavel

AU - Its, Alexander

TI - Asymptotics of the partition function of a random matrix model

JO - Annales de l’institut Fourier

PY - 2005

PB - Association des Annales de l'Institut Fourier

VL - 55

IS - 6

SP - 1943

EP - 2000

AB - We prove a number of results concerning the large $N$ asymptotics of the free energy of a
random matrix model with a polynomial potential. Our approach is based on a deformation
of potential and on the use of the underlying integrable structures of the matrix model.
The main results include the existence of a full asymptotic expansion in even powers of
$N$ of the recurrence coefficients of the related orthogonal polynomials for a one-cut
regular potential and the double scaling asymptotics of the free energy for a singular
quartic potential. We also prove the analyticity of the coefficients of the asymptotic
expansions of the recurrence coefficients and the free energy, with respect to the
coefficients of the potential, and the one-sided analyticity of the recurrent
coefficients and the free energy for a one-cut singular potential.

LA - eng

KW - Matrix Models; orthogonal polynomials; partition function

UR - http://eudml.org/doc/116239

ER -

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