Variational formula for the logarithmic potential of free additive convolutions
- Belius, David ORCID UniDistance Suisse
- Concetti, Francesco
- Genovese, Giuseppe
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2025
English
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.
- Identifiers
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- DOI 10.48550/ARXIV.2506.19064
- URI https://pub.orcid.org/v3.0/0000-0003-3706-043X/work/207851121
- ARK ark:/51647/srd1336037
- Persistent URL
- https://n2t.net/ark:/51647/srd1336037
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