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http://cimat.repositorioinstitucional.mx/jspui/handle/1008/600| On the Non-Classical Infinite Divisibility of Power Semicircle Distribution | |
| VICTOR MANUEL PEREZ ABREU CARRION | |
| Acceso Abierto | |
| Atribución-NoComercial | |
| Probabilidad Algebras - Operadores | |
| Abstract. The family of power semicircle distributions de fi ned as normal- ized real powers of the semicircle density is considered. The marginals of uniform distributions on spheres in high-dimensional Euclidean spaces are included in this family and a boundary case is the classical Gaussian dis- tribution. A review of some results including a genesis and the so-called Poincaré’s theorem is presented. The moments of these distributions are re- lated to the super Catalan numbers and their Cauchy transforms in terms of hypergeometric functions are derived. Some members of this class of dis- tributions play the role of the Gaussian distribution with respect to additive convolutions in non-commutative probability, such as the free, the monotone, the anti-monotone and the Boolean convolutions. The in fi nite divisibility of other power semicircle distributions with respect to these convolutions is stud- ied using simple kurtosis arguments. A connection between kurtosis and the free divisibility indicator is found. It is shown that for the classical Gaussian distribution the free divisibility indicator is strictly less than 2. | |
| Centro de Investigación en Matemáticas AC | |
| 17-03-2010 | |
| Reporte | |
| Inglés | |
| Investigadores | |
| TEORÍA ANALÍTICA DE LA PROBABILIDAD | |
| Versión publicada | |
| publishedVersion - Versión publicada | |
| Aparece en las colecciones: | Reportes Técnicos - Probabilidad y Estadística |
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