The free energy of matrix models

• 成果类型: Article
• 署名作者: Parraud, Felix; Schnelli, Kevin
• 署名单位: Royal Institute of Technology
• 刊物名称: PROBABILITY THEORY AND RELATED FIELDS
• ISSN/ISSBN: 0178-8051
• DOI: 10.1007/s00440-025-01400-w
• 发表日期: 2025
• 页码: 427-482
• 关键词: information measure; free entropy; asymptotics; INTEGRALS; analogs

摘要

In this paper we study multi-matrix models whose potentials are perturbations of the quadratic potential associated with independent GUE random matrices. More precisely, we compute the free energy and the expectation of the trace of polynomials evaluated in those matrices. We prove an asymptotic expansion in the inverse of the matrix dimension to any order. Out of this result we deduce new formulas for map enumerations and the microstates free entropy. Our approach is based on the interpolation method between random matrices and free operators developed in Collins et al. (Camb J Math 10: 195-260, 2022) and Parraud (Commun Math Phys 399: 1-46, 2022).