Samuel G. G. Johnston

Free probability via entropic optimal transport

Abstract Let $\mu $ μ and $\nu $ ν be compactly supported probability measures on ℝ, and let $\mu \boxplus \nu $ μ ⊞ ν denote their additive free convolution. We show that for all sufficiently large real $z$ z , $$ \int _{-\infty }^{\infty }\log (z - x) \, (\mu \boxplus \nu )( \m...