Generalized random matrix model with additional interactions

We introduce a log-gas model that is a generalization of a random matrix ensemble with an additional interaction, whose strength depends on a parameter $γ$. The equilibrium density is computed by numerically solving the Riemann-Hilbert problem associated with the ensemble. The effect of the additional parameter $γ$ associated with the two-body interaction can be understood in terms of an effective $γ$-dependent single-particle confining potential.

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