For compactly supported probability measures, the logarithmic potential of their free additive convolution equals the minimum of an explicit variational energy, with explicit forms for semicircle and Marchenko-Pastur convolutions.
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Variational formula for the logarithmic potential of free additive convolutions
For compactly supported probability measures, the logarithmic potential of their free additive convolution equals the minimum of an explicit variational energy, with explicit forms for semicircle and Marchenko-Pastur convolutions.