Generalized approach to the non-backtracking lace expansion

• 成果类型: Article
• 署名作者: Fitzner, Robert; van der Hofstad, Remco
• 署名单位: Eindhoven University of Technology
• 刊物名称: PROBABILITY THEORY AND RELATED FIELDS
• ISSN/ISSBN: 0178-8051
• DOI: 10.1007/s00440-016-0747-8
• 发表日期: 2017
• 页码: 1041-1119
• 关键词: self-avoiding walk; upper critical dimension; field critical-behavior; percolation models; triangle condition; lattice animals; contact process; ising-model; inequalities; trees

摘要

The lace expansion is a powerful perturbative technique to analyze the critical behavior of random spatial processes such as the self-avoiding walk, percolation and lattice trees and animals. The non-backtracking lace expansion (NoBLE) is a modification that allows us to improve its applicability in the nearest-neighbor setting on the -lattice for percolation, lattice trees and lattice animals. The NoBLE gives rise to a recursive formula that we study in this paper at a general level. We state assumptions that guarantee that the solution of this recursive formula satisfies the infrared bound. In two related papers, we show that these conditions are satisfied for percolation in , for lattice trees in and for lattice animals in d >= 18.