Critical large deviations in harmonic crystals with long-range interactions

• 成果类型: Article
• 署名作者: Caputo, P; Deuschel, JD
• 署名单位: Technical University of Berlin
• 刊物名称: ANNALS OF PROBABILITY
• ISSN/ISSBN: 0091-1798
• 发表日期: 2001
• 页码: 242-287
• 关键词: walks

摘要

We continue our study of large deviations of the empirical measures of a massless Gaussian field on Z(d), whose covariance is given by the Green function of a long-range random walk. In this paper we extend techniques and results of Bolthausen and Deuschel to the nonlocal case of a random walk in the domain of attraction of the symmetric alpha -stable law, with alpha epsilon (0, 2 boolean AND d). In particular, we show that critical large deviations occur at the capacity scale Nd-alpha, With a rate function given by the Dirichlet form of the embedded alpha -stable process. We also prove that if we impose zero boundary conditions, the rate function is given by the Dirichlet form of the killed alpha -stable process.