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

J. Armando Dominguez-Molina (Universidad Autónoma de Sinaloa)
Víctor Pérez-Abreu (Centro de Investigación en Matemáticas)
Alfonso Rocha-Arteaga (Universidad Autónoma de Sinaloa)


It is known that the so-called Bercovici-Pata bijection can be explained in terms of certain Hermitian random matrix ensembles (Md)d≥1 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 sample path approximation by covariation processes for these matrix Lévy processes is obtained. As a general result we prove that any d×d complex matrix subordinator with jumps of rank one is the quadratic variation of a $\mathbb{C}^d$-valued Lévy process. In particular, we have the corresponding result for matrix subordinators with jumps of rank one associated to the random matrix ensembles (Md)d≥1.

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Pages: 1-14

Publication Date: January 17, 2013

DOI: 10.1214/ECP.v18-2113


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