# Universality Conjecture and Results for a Model of Several Coupled Positive-Definite Matrices

@article{Bertola2014UniversalityCA, title={Universality Conjecture and Results for a Model of Several Coupled Positive-Definite Matrices}, author={Marco Bertola and Thomas Bothner}, journal={Communications in Mathematical Physics}, year={2014}, volume={337}, pages={1077-1141} }

The paper contains two main parts: in the first part, we analyze the general case of $${p \geq 2}$$p≥2 matrices coupled in a chain subject to Cauchy interaction. Similarly to the Itzykson-Zuber interaction model, the eigenvalues of the Cauchy chain form a multi level determinantal point process. We first compute all correlations functions in terms of Cauchy biorthogonal polynomials and locate them as specific entries of a $${(p+1) \times (p+1)}$$(p+1)×(p+1) matrix valued solution of a Riemann…

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