Asymptotics of the partition function of a random matrix model

Simple item page
dc.creatorBleher, Pavel
dc.creatorIts, Alexander
dc.date2004-09-30
dc.date.accessioned2026-07-07T04:31:30Z
dc.date.available2026-07-07T04:31:30Z
dc.descriptionWe prove a number of results concerning the large $N$ asymptotics of the free energy of a random matrix model with a polynomial potential $V(z)$. Our approach is based on a deformation $τ_tV(z)$ of $V(z)$ to $z^2$, $0\le t<\infty$ and on the use of the underlying integrable structures of the matrix model. The main results include (1) the existence of a full asymptotic expansion in powers of $N^{-2}$ of the recurrence coefficients of the related orthogonal polynomials, for a one-cut regular $V$; (2) the existence of a full asymptotic expansion in powers of $N^{-2}$ of the free energy, for a $V$, which admits a one-cut regular deformation $τ_tV$; (3) the analyticity of the coefficients of the asymptotic expansions of the recurrence coefficients and the free energy, with respect to the coefficients of $V$; (4) the one-sided analyticity of the recurrent coefficients and the free energy for a one-cut singular $V$; (5) the double scaling asymptotics of the free energy for a singular quartic polynomial $V$.
dc.description43 pages, 3 figures
dc.identifierhttps://arxiv.org/abs/math-ph/0409082
dc.identifierhttp://arxiv.org/abs/math-ph/0409082
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/57837
dc.subjectMathematical Physics
dc.subject82B23
dc.titleAsymptotics of the partition function of a random matrix model
dc.typetext

Files

Collections

arXiv