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Covariation representations for Hermitian Lévy process ensembles of free infinitely divisible distributions

Covariation representations for Hermitian Lévy process ensembles of free infinitely divisible distributions

It is known that the so-called Bercovici-Pata bijection can be explained in terms of certain Hermitian random matrix ensembles (M<sub>d</sub>)<sub>d≥1</sub> whose asymptotic spectral distributions are free infinitely divisible. We investigate Hermitian Lévy processes with jumps of rank one associated to these random matrix ensembles introduced by Benaych-Georges and Cabanal-Duvillard. A …