INTERMITTENCY FOR BRANCHING RANDOM WALK IN PARETO ENVIRONMENT

• 成果类型: Article
• 署名作者: Ortgiese, Marcel; Roberts, Matthew I.
• 署名单位: University of Munster; University of Bath
• 刊物名称: ANNALS OF PROBABILITY
• ISSN/ISSBN: 0091-1798
• DOI: 10.1214/15-AOP1021
• 发表日期: 2016
• 页码: 2198-2263
• 关键词: parabolic anderson model; THEOREM

摘要

We consider a branching random walk on the lattice, where the branching rates are given by an i.i.d. Pareto random potential. We describe the process, including a detailed shape theorem, in terms of a system of growing lilypads. As an application we show that the branching random walk is intermittent, in the sense that most particles are concentrated on one very small island with large potential. Moreover, we compare the branching random walk to the parabolic Anderson model and observe that although the two systems show similarities, the mechanisms that control the growth are fundamentally different.