NOISE-STABILITY AND CENTRAL LIMIT THEOREMS FOR EFFECTIVE RESISTANCE OF RANDOM ELECTRIC NETWORKS

• 成果类型: Article
• 署名作者: Rossignol, Raphael
• 署名单位: Communaute Universite Grenoble Alpes; Universite Grenoble Alpes (UGA); Centre National de la Recherche Scientifique (CNRS); CNRS - National Institute for Mathematical Sciences (INSMI)
• 刊物名称: ANNALS OF PROBABILITY
• ISSN/ISSBN: 0091-1798
• DOI: 10.1214/14-AOP996
• 发表日期: 2016
• 页码: 1053-1106
• 关键词: normal approximation; BOOLEAN FUNCTIONS; homogenization; variance; conductance

摘要

We investigate the (generalized) Walsh decomposition of point-to-point effective resistances on countable random electric networks with i.i.d. resistances. We show that it is concentrated on low levels, and thus point-to-point effective resistances are uniformly stable to noise. For graphs that satisfy some homogeneity property, we show in addition that it is concentrated on sets of small diameter. As a consequence, we compute the right order of the variance and prove a central limit theorem for the effective resistance through the discrete torus of side length n in Z(d), when n goes to infinity.