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http://cimat.repositorioinstitucional.mx/jspui/handle/1008/903| Functional limit theorems for trace processes in a Dyson Brownian motion | |
| VICTOR MANUEL PEREZ ABREU CARRION | |
| Acceso Abierto | |
| Atribución-NoComercial-CompartirIgual | |
| Movimiento Browniano | |
| In this paper we study functional asymptotic behavior of p-trace processes of n £ n Hermitian matrix valued Brownian motions, when n goes to in¯nity. For each p ¸ 1 we establish uniform a.s. and Lq laws of large numbers and study the a.s. convergence of the supremum (respectively in¯- mum) over a compact interval of the largest (respectively smallest) eigenvalue process. We also prove that the °uctuations around the limiting process, converge weakly to a one-dimensional centered Gaussian process Zp, given as a Wiener integral with a deterministic Volterra kernel. This process depends on Zp¡1; :::;Z1 and a Gaussian martingale of independent interest whose increasing process is explicitly derived. Our approach is based on stochastic analysis and semimartingales tools. | |
| Serials Publications | |
| 2007 | |
| Artículo | |
| Inglés | |
| Investigadores | |
| OTRAS | |
| Versión publicada | |
| publishedVersion - Versión publicada | |
| Aparece en las colecciones: | Probababilidad Y Estadística |
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