Asymptotics of the partition function of a Laguerre-type random matrix model

TL;DR

This paper derives the large-size asymptotic expansion of the partition function for a Laguerre-type random matrix model using Riemann-Hilbert analysis, revealing detailed behavior as matrix size grows.

Contribution

It provides the first detailed asymptotic expansion of the partition function for this class of random matrix models using advanced analytical techniques.

Findings

Asymptotic expansion of log Z_N in powers of N^{-2}

Application of Deift-Zhou steepest descent method to Laguerre-type models

Enhanced understanding of large N behavior in random matrix theory

Abstract

We study asymptotics of the partition function $Z_N$ of a Laguerre-type random matrix model when the matrix order $N$ tends to infinity. By using the Deift-Zhou steepest descent method for Riemann-Hilbert problems, we obtain an asymptotic expansion of $\log Z_N$ in powers of $N^{-2}$.