Growing in time IDLA cluster is recurrent

Electronic Communications in Probability

Ruojun Huang¹ 

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

DOI  :  10.1214/19-ECP233

学科分类：统计和概率

来源: Institute of Mathematical Statistics

【 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 $d\ge 3$.

【 授权许可】

CC BY