MULTI-SCALE LIPSCHITZ PERCOLATION OF INCREASING EVENTS FOR POISSON RANDOM WALKS

• 成果类型: Article
• 署名作者: Gracar, Peter; Stauffer, Alexandre
• 署名单位: University of Cologne; University of Bath
• 刊物名称: ANNALS OF APPLIED PROBABILITY
• ISSN/ISSBN: 1050-5164
• DOI: 10.1214/18-AAP1420
• 发表日期: 2019
• 页码: 376-433
• 关键词: spread

摘要

Consider the graph induced by Z(d), equipped with uniformly elliptic random conductances. At time 0, place a Poisson point process of particles on Z(d) and let them perform independent simple random walks. Tessellate the graph into cubes indexed by i is an element of Z(d) and tessellate time into intervals indexed by tau. Given a local event E(i, tau) that depends only on the particles inside the space time region given by the cube i and the time interval tau, we prove the existence of a Lipschitz connected surface of cells (i, tau) that separates the origin from infinity on which E(i, tau) holds. This gives a directly applicable and robust framework for proving results in this setting that need a multi-scale argument. For example, this allows us to prove that an infection spreads with positive speed among the particles.