Matrix models at low temperature
Abstract
In this article, we investigate the behavior of multi-matrix models under a potential V β = βU + W when the inverse temperature β becomes very large.We first prove, under mild hypothesis on the functionals U, W , that as soon as these potentials are "confining" at infinity, the norm of these random matrices stays uniformly bounded with large probability.As a consequence, the sequence of their non-commutative distributions is tight when the dimension goes to infinity.We show that their limit points satisfy the Dyson-Schwinger equations.Next we investigate a few specific models, most importantly the "strong single variable model" where U is a sum of potentials in a single matrix and the "strong commutator model" where U = -[X, Y ] 2 .
Fields of Study & Subjects
Random Matrices and Applications
Spectral Theory in Mathematical Physics
Theoretical and Computational Physics
Publication details
- Journal / source
- Latin American Journal of Probability and Mathematical Statistics
- Volume
- 23
- Issue
- 2
- Pages
- 801–801
- Publication date
- 1 January 2026
- Language
- EN