Título
Functional limit theorems for trace processes in a Dyson Brownian motion
Autor
VICTOR MANUEL PEREZ ABREU CARRION
Nivel de Acceso
Acceso Abierto
Materias
Resumen o descripción
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.
Editor
Serials Publications
Fecha de publicación
2007
Tipo de publicación
Artículo
Versión de la publicación
Versión publicada
Recurso de información
Formato
application/pdf
Idioma
Inglés
Audiencia
Investigadores
Repositorio Orígen
Repositorio Institucional CIMAT
Descargas
299