PLANAR ISING MAGNETIZATION FIELD I. UNIQUENESS OF THE CRITICAL SCALING LIMIT

• 成果类型: Article
• 署名作者: Camia, Federico; Garban, Christophe; Newman, Charles M.
• 署名单位: Vrije Universiteit Amsterdam; New York University; New York University Abu Dhabi; Centre National de la Recherche Scientifique (CNRS); Ecole Normale Superieure de Lyon (ENS de LYON); New York University; Vrije Universiteit Amsterdam; University of California System; University of California Irvine
• 刊物名称: ANNALS OF PROBABILITY
• ISSN/ISSBN: 0091-1798
• DOI: 10.1214/13-AOP881
• 发表日期: 2015
• 页码: 528-571
• 关键词: infinite conformal symmetry; erased random-walks; critical percolation; Invariance; cluster; sle; fluctuations; bounds; MODEL

摘要

The aim of this paper is to prove the following result. Consider the critical Ising model on the resealed grid aZ(2), then the renormalized magnetization field Phi(a) := a(15/8)s Sigma(x is an element of aZ2)sigma(x)delta(x), seen as a random distribution (i.e., generalized function) on the plane, has a unique scaling limit as the mesh size a SE arrow 0. The limiting field is conformally covariant.