Large deviations upper bounds for the laws of matrix-valued processes and non-communicative entropies

• 成果类型: Article
• 署名作者: Duvillard, TC; Guionnet, A
• 署名单位: Universite Paris Cite; Ecole Normale Superieure de Lyon (ENS de LYON)
• 刊物名称: ANNALS OF PROBABILITY
• ISSN/ISSBN: 0091-1798
• 发表日期: 2001
• 页码: 1205-1261
• 关键词: free probability-theory; fisher information measure; analogs; limit

摘要

Using It (o) over caps calculus, we study the large deviations properties of the law of the spectral measure of the Hermitian Brownian motion. We extend this strategy to the symmetric, unitary and Wishart processes. This dynamical approach is generalized to the study of the large deviations of the non-commutative laws of several independent Hermitian Brownian motions. As a consequence, we can bound from above entropies defined in the spirit of the microstates entropy introduced by Voiculescu.