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http://cimat.repositorioinstitucional.mx/jspui/handle/1008/613| Almost sure and -convergence of the traces of Laguerre processes to the family of dilations of the standard free Poisson distribution are established. We also prove that the fl uctuations around the limiting proces s, converge weakly to a continuous centered Gaussian process. The almost sure convergence on compact time intervals of the largest and smallest eigenvalues processes is also established | |
| VICTOR MANUEL PEREZ ABREU CARRION | |
| Acceso Abierto | |
| Atribución-NoComercial | |
| Probabilidad | |
| F ree In nite Divisibility of Free Multiplicative Mixtures of the Wigner Distribution Victor Perez-Abreu ∗ Department of Probability and Statistics, CIMAT Apdo. Postal 402, Guanajuato Gto. 36000, Mexico pabreu@cimat.mx Noriyoshi Sakuma † Department of Mathematics, Keio University, 3-14-1, Hiyoshi, Yokohama 223-8522, Japan. noriyosi@math.keio.ac.jp March 19, 2010 Abstract Let I and I be the classes of all classical in nitely divisible distributions and free in nitely divisible distributions, respectively, and let be the Bercovici-Pata bijection between I and I : The class type W of symmetric distributions in I that can be represented as free multiplicative convolutions of the Wigner distribution is studied. A characterization of this class under the condition that the mixing distribution is 2-divisible with respect to free multiplicative convolution is given. A correspondence between sym- metric distributions in I and the free counterpart under of the positive distributions in I is established. It is shown that the class type W does not include all symmetric distributions in I and that it does not coincide with the image under of the mixtures of the Gaussian distribution in I . Similar results for free multiplicative convolutions with the symmetric arcsine measure are obtained. Several well-known and new concrete examples are presented | |
| Centro de Investigación en Matemáticas AC | |
| 15-10-2009 | |
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| publishedVersion - Versión publicada | |
| Aparece en las colecciones: | Reportes Técnicos - Probabilidad y Estadística |
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