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Published online by Cambridge University Press: 29 May 2025
We give a summary of the recent progress made by the authors and collaborators on the asymptotic analysis of the two-matrix model with a quartic potential. The paper also contains a list of open problems.
1. Two-matrix model: introduction
The Hermitian two-matrix model is the probability measure
defined on pairs (M1> , M2) of n× n Hermitian matrices. Here V and W are two polynomial potentials, τ ≠ 0 is a coupling constant, and
is a normalization constant in order to make (1-1) a probability measure.
In recent works of the authors and collaborators [Duits et al. 2011; 2012;
Duits and Kuijlaars 2009; Mo 2009] the model was studied with the aim to gain
understanding in the limiting behavior of the eigenvalues of M1 as n→∞, and
to find and describe new types of critical behaviors.
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