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Rank-One HCIZ Integrals and Multiplicative Convolutions
We study how spectral averaging interacts with the logarithm in large-dimensional rank-one Harish-Chandra--Itzykson--Zuber (HCIZ) integrals. For independent bi-unitarily invariant matrices $A,B$ with uniformly bounded deterministic singular values and weakly convergent empirical spectral measures of
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