Work

Asymptotics of the partition function of the perturbed Gross–Witten–Wadia unitary matrix model

Year: 2024

Type: article

Abstract: We consider the asymptotics of the partition function of the extended Gross–Witten–Wadia unitary matrix model by introducing an extra logarithmic term in the potential. The partition function can be written as a Toeplitz determinant with entries expressed in terms of the modified Bessel functions of the first kind and furnishes a ‐function sequence of the Painlevé equation. We derive the asymptotic expansions of the Toeplitz determinant up to and including the constant terms as the size of the determinant tends to infinity. The constant terms therein are expressed in terms of the Riemann zeta‐function and the Barnes ‐function. A third‐order phase transition in the leading terms of the asymptotic expansions is also observed.

Source: Studies in Applied Mathematics

DOI: 10.1111/sapm.12762

Authors: Yu Chen, Shuai‐Xia Xu, Yu‐Qiu Zhao

Institutions: Qilu University of Technology, Sun Yat-sen University, Shandong Academy of Sciences, Institut Franco-Chinois de l'Energie Nucléaire

Language: English

Topic: Random Matrices and Applications

Subfield: Statistics and Probability

Field: Mathematics

Domain: Physical Sciences

Open Access status: green

Funders: National Natural Science Foundation of China, Basic and Applied Basic Research Foundation of Guangdong Province