2025/06/23 by Francesco Concetti, Concetti, Francesco, David Belius +3
Mathematics · #Numerical methods in inverse problems #Spectral Theory in Mathematical Physics #Differential Equations and Boundary Problems
paper · pdf · doi:10.48550/arxiv.2506.19064
We establish a general variational formula for the logarithmic potential of the free additive convolution of two compactly supported probability measure on \R. The formula is given in terms of the R-transform of the first measure, and the logarithmic potential of second measure. The result applies in particular to the additive convolution with the semicircle or Marchenko-Pastur laws, for which the formula simplifies. The logarithmic potential of additive convolutions appears for instance in estimates of the determinant of sums of independent random matrices.