SCALING LIMIT OF THE SUBDIFFUSIVE RANDOM WALK ON A GALTON-WATSON TREE IN RANDOM ENVIRONMENT

• 成果类型: Article
• 署名作者: de Raphelis, Loic
• 署名单位: Ecole Normale Superieure de Lyon (ENS de LYON)
• 刊物名称: ANNALS OF PROBABILITY
• ISSN/ISSBN: 0091-1798
• DOI: 10.1214/21-AOP1535
• 发表日期: 2022
• 页码: 339-396
• 关键词: theorem; GROWTH

摘要

We consider a random walk on a Galton-Watson tree in random environment, in the subdiffusive case. We prove the convergence of the renormalised height function of the walk towards the continuous-time height process of a spectrally positive strictly stable Levy process, jointly with the convergence of the renormalised trace of the walk towards the real tree coded by the latter continuous-time height process.