| Título: | Covariation representations for Hermitian Lévy process ensembles of free infinitely divisible distributions |
| Autores: |
Dominguez-Molina, J. Armando; Universidad Autónoma de Sinaloa Pérez-Abreu, Víctor; Centro de Investigación en Matemáticas Rocha-Arteaga, Alfonso; Universidad Autónoma de Sinaloa |
| Fecha: | 2013-01-03 |
| Publicador: | Electronic Communications in Probability |
| Fuente: |
Ver documento |
| Tipo: | Peer-reviewed Article |
| Tema: |
Infinitely divisible random matrix, matrix subordinator, Bercovici-Pata bijection, matrix semimartingale, matrix compound Poisson. 60B20; 60E07; 60G51; 60G57. |
| Descripción: | 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. |
| Idioma: | Inglés |
1 On the Non-Convexity of the Time Constant in First-Passage Percolation por Kesten, Harry; Cornell University | 6 Simulations and Conjectures for Disconnection Exponents por Puckette, Emily E.; Occidental College,Werner, Wendelin; Université Paris-Sud and IUF |
2 A Proof of a Conjecture of Bobkov and Houdré por Kwapien, S.; Warsaw University,Pycia, M.; Warsaw University,Schachermayer, W.; University of Vienna | 7 Excursions Into a New Duality Relation for Diffusion Processes por Jansons, Kalvis M.; University College London |
3 Moderate Deviations for Martingales with Bounded Jumps por Dembo, Amir; Stanford University | 8 Percolation Beyond $Z^d$, Many Questions And a Few Answers por Benjamini, Itai; Weizmann Institute of Science,Schramm, Oded; Microsoft Research |
4 Bounds for Disconnection Exponents por Werner, Wendelin; Université Paris-Sud and IUF | 9 Transportation Approach to Some Concentration Inequalities in Product Spaces por Dembo, Amir; Stanford University,Zeitouni, Ofer; Technion - Israel Institute of Technology |
5 The Dimension of the Frontier of Planar Brownian Motion por Lawler, Gregory F.; Duke University | 10 Surface Stretching for Ornstein Uhlenbeck Velocity Fields por Carmona, Rene; Princeton University,Grishin, Stanislav; Princeton University,Xu, Lin; Princeton University,Molchanov, Stanislav; University of North Carolina at Charlotte |