Approximation of subadditive functions and convergence rates in limiting-shape results

• 成果类型: Article; Proceedings Paper
• 署名作者: Alexander, KS
• 署名单位: University of Southern California
• 刊物名称: ANNALS OF PROBABILITY
• ISSN/ISSBN: 0091-1798
• 发表日期: 1997
• 页码: 30-55
• 关键词: statistical mechanical methods; particle structure-analysis; lattice field-theories; bernoulli percolation

摘要

For a nonnegative subadditive function h on Z(d), with limiting approximation g(x) = lim(n) h(nx)/n, it is of interest to obtain bounds on the discrepancy between g(x) and h(x), typically of order \x\(nu) with nu < 1. For certain subadditive h(x), particularly those which are expectations associated with optimal random paths from 0 to x, in a somewhat standardized way a more natural and seemingly weaker property can be established: every x is in a bounded multiple of the convex hull of the set of sites satisfying a similar bound. me show that this convex-hull property implies the desired bound for all x. Applications include rates of convergence in limiting-shape results for first-passage percolation (standard and oriented) and longest common subsequences and bounds on the error in the exponential-decay approximation to the off-axis connectivity function for subcritical Bernoulli bond percolation on the integer lattice.