Euclidean Gibbs measures on loop lattices: Existence and a priori estimates

• 成果类型: Article
• 署名作者: Albeverio, S; Kondratiev, Y; Pasurek, T; Röckner, M
• 署名单位: University of Bonn; University of Bielefeld; University of Bielefeld
• 刊物名称: ANNALS OF PROBABILITY
• ISSN/ISSBN: 0091-1798
• 发表日期: 2004
• 页码: 153-190
• 关键词: elliptic-equations; invariant-measures; quantum crystal; uniqueness; STATES; systems; ergodicity; DYNAMICS; FIELDS; SPACE

摘要

We present a new method to prove existence and uniform a priori estimates for Euclidean Gibbs measures corresponding to quantum anharmonic crystals. It is based first on the alternative characterization of Gibbs measures in terms of their logarithmic derivatives through integration by parts formulas, and second on the choice of appropriate Lyapunov functionals.