Exact asymptotics for some probability distributions on compact manifolds

• 成果类型: Article
• 署名作者: Richards, DSP
• 刊物名称: ANNALS OF STATISTICS
• ISSN/ISSBN: 0090-5364
• DOI: 10.1214/aos/1176324313
• 发表日期: 1995
• 页码: 1582-1586
• 关键词: reduced phase-space; symplectic form; co-homology

摘要

Let M be a compact, smooth, orientable manifold without boundary, and let f: M --> R be a smooth function. Let dm be a volume form on M with total volume 1, and denote by X the corresponding random variable. Using a theorem of Kirwan, we obtain necessary conditions under which the method of stationary phase returns an exact evaluation of the characteristic function of f(X). As an application to the Langevin distribution on the sphere S-d-1, We deduce that the method of stationary phase provides an exact evaluation of the normalizing constant for that distribution when, and only when, d is odd.