A CONTINUOUS SEMIGROUP OF NOTIONS OF INDEPENDENCE BETWEEN THE CLASSICAL AND THE FREE ONE

• 成果类型: Article
• 署名作者: Benaych-Georges, Florent; Levy, Thierry
• 署名单位: Universite Paris Cite; Sorbonne Universite; Institut Polytechnique de Paris; Ecole Polytechnique; Centre National de la Recherche Scientifique (CNRS); Universite PSL; Ecole Normale Superieure (ENS)
• 刊物名称: ANNALS OF PROBABILITY
• ISSN/ISSBN: 0091-1798
• DOI: 10.1214/10-AOP573
• 发表日期: 2011
• 页码: 904-938
• 关键词: calculus

摘要

In this paper, we investigate a continuous family of notions of independence which interpolates between the classical and free ones for noncommutative random variables. These notions are related to the liberation process introduced by Voiculescu. To each notion of independence correspond new convolutions of probability measures, for which we establish formulae and of which we compute simple examples. We prove that there exists no reasonable analogue of classical and free cumulants associated to these notions of independence.