Stochastic areas, winding numbers and Hopf fibrations

• 成果类型: Article
• 署名作者: Baudoin, Fabrice; Wang, Jing
• 署名单位: University of Connecticut; University of Illinois System; University of Illinois Urbana-Champaign
• 刊物名称: PROBABILITY THEORY AND RELATED FIELDS
• ISSN/ISSBN: 0178-8051
• DOI: 10.1007/s00440-016-0745-x
• 发表日期: 2017
• 页码: 977-1005
• 关键词: atiyah-singer theorems; probabilistic approach

摘要

We define and study stochastic areas processes associated with Brownian motions on the complex symmetric spaces and . The characteristic functions of those processes are computed and limit theorems are obtained. In the case , we also study windings of the Brownian motion on those spaces and compute the limit distributions. For the geometry of the Hopf fibration plays a central role, whereas for it is the anti-de Sitter fibration.