Large deviation bounds for matrix Brownian motion

• 成果类型: Article
• 署名作者: Biane, P; Capitaine, M; Guionnet, A
• 署名单位: Centre National de la Recherche Scientifique (CNRS); Universite PSL; Ecole Normale Superieure (ENS); Universite de Toulouse; Universite Toulouse III - Paul Sabatier; Ecole Normale Superieure de Lyon (ENS de LYON)
• 刊物名称: INVENTIONES MATHEMATICAE
• ISSN/ISSBN: 0020-9910
• DOI: 10.1007/s00222-002-0281-4
• 发表日期: 2003
• 页码: 433-459
• 关键词: information measure; entropy; analogs

摘要

We prove large deviation bounds for the convergence of Hermitian matrix valued Brownian motion towards free Brownian motion. As a consequence, we obtain upper and lower bounds on the microstates entropy introduced by Voiculescu [24].