Growing in time IDLA cluster is recurrent

[摘要] We show that Internal Diffusion Limited Aggregation (IDLA )on $\mathbb{Z} ^{d}$ has near optimal Cheeger constant when the growing cluster is large enough. This implies, through a heat kernel lower bound derived previously in [11], that simple random walk evolving independently on growing in time IDLA cluster is recurrent when $d\ge 3$.

[学科分类] 统计和概率

[关键词] isoperimetry;internal diffusion limited aggregation;recurrence;random walk;random environment;changing environment