A variational principle for a non-integrable model

• 成果类型: Article
• 署名作者: Menz, Georg; Tassy, Martin
• 署名单位: University of California System; University of California Los Angeles; Dartmouth College
• 刊物名称: PROBABILITY THEORY AND RELATED FIELDS
• ISSN/ISSBN: 0178-8051
• DOI: 10.1007/s00440-020-00959-w
• 发表日期: 2020
• 页码: 747-822
• 关键词: limit shapes; statistics; tilings

摘要

We show the existence of a variational principle for graph homomorphisms from Z(m) to a d-regular tree. The technique is based on a discrete Kirszbraun theorem and a concentration inequality obtained through the dynamics of the model. As another consequence of the concentration inequality we also obtain the existence of a continuum of translation-invariant ergodic gradient Gibbs measures for graph homomorphisms from Z(m) to a regular tree. The method is sufficiently robust such that it could be applied to other discrete models with a quite general target graphs.