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We consider several limiting cases of the joint probability distribution for a random matrix ensemble with an additional interaction term controlled by an exponent γ (called the γ ensembles). The effective potential, which is essentially the single-particle confining potential for an equivalent ensemble with γ=1 (called the Muttalib-Borodin ensemble), is a crucial quantity defined in solution to the Riemann-Hilbert problem associated with the γ ensembles. It enables us to numerically compute the eigenvalue density of γ ensembles for all
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