BIASED RANDOM WALK ON DYNAMICAL PERCOLATION

• 成果类型: Article
• 署名作者: Andres, Sebastian; Gantert, Nina; Schmid, Dominik; Sous, Perla
• 署名单位: Braunschweig University of Technology; Technical University of Munich; University of Bonn; University of Cambridge
• 刊物名称: ANNALS OF PROBABILITY
• ISSN/ISSBN: 0091-1798
• DOI: 10.1214/23-AOP1679
• 发表日期: 2024
• 页码: 2051-2078
• 关键词: speed; diffusion; range; times; drift

摘要

We study biased random walks on dynamical percolation on Zd. We establish a law of large numbers and an invariance principle for the random walk using regeneration times. Moreover, we verify that the Einstein relation holds, and we investigate the speed of the walk as a function of the bias. While for d = 1 the speed is increasing, we show that, in general, this fails in dimension d >= 2. As our main result, we establish two regimes of parameters, separated by an explicit critical curve such that the speed is either eventually strictly increasing or eventually strictly decreasing. This is in sharp contrast to the biased random walk on a static supercritical percolation cluster where the speed is known to be eventually zero.