BIASED RANDOM WALK IN POSITIVE RANDOM CONDUCTANCES ON Zd

• 成果类型: Article
• 署名作者: Fribergh, Alexander
• 署名单位: Universite Federale Toulouse Midi-Pyrenees (ComUE); Universite de Toulouse; Institut National des Sciences Appliquees de Toulouse; Centre National de la Recherche Scientifique (CNRS); Universite de Toulouse
• 刊物名称: ANNALS OF PROBABILITY
• ISSN/ISSBN: 0091-1798
• DOI: 10.1214/13-AOP835
• 发表日期: 2013
• 页码: 3910-3972
• 关键词: einstein relation; percolation; diffusion

摘要

We study the biased random walk in positive random conductances on Z(d). This walk is transient in the direction of the bias. Our main result is that the random walk is ballistic if, and only if, the conductances have finite mean. Moreover, in the sub-ballistic regime we find the polynomial order of the distance moved by the particle. This extends results obtained by Shen [Ann. Appl. Probab. 12 (2002) 477-510], who proved positivity of the speed in the uniformly elliptic setting.