Diagrammatic bounds on the lace-expansion coefficients for oriented percolation

2007/08/21 by Akira Sakai, Sakai, Akira
Mathematics · #60K35 #82B27 #Advanced Combinatorial Mathematics #FOS: Mathematics #FOS: Physical sciences #Mathematical Physics (math-ph) #Probability (math.PR) #Random Matrices and Applications #Stochastic processes and statistical mechanics

paper · pdf · doi:10.48550/arxiv.0708.2897

openalex publication_date 2007/08/21 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We provide a complete proof of the diagrammatic bounds on the lace-expansion coefficients for oriented percolation, which are used in [arXiv:math/0703455] to investigate critical behavior for long-range oriented percolation above 2minα,2 spatial dimensions.

Related

• Asymptotic expansion of the critical point for oriented percolation in high dimensions
• Critical behavior and the limit distribution for long-range oriented percolation. II: Spatial correlation
• SLE(6) and CLE(6) from Critical Percolation
• Mean-field behavior for nearest-neighbor percolation in d>10
• An extension of the inductive approach to the lace expansion