CONVERGENCE OF THE RANDOM ABELIAN SANDPILE

• 成果类型: Article
• 署名作者: Bou-Rabee, Ahmed
• 署名单位: University of Chicago
• 刊物名称: ANNALS OF PROBABILITY
• ISSN/ISSBN: 0091-1798
• DOI: 10.1214/21-AOP1528
• 发表日期: 2021
• 页码: 3168-3196
• 关键词: stochastic homogenization; elliptic-equations

摘要

We prove that Abelian sandpiles with random initial states converge almost surely to unique scaling limits. The proof follows the Armstrong-Smart program for stochastic homogenization of uniformly elliptic equations. Using simple random walk estimates, we prove an analogous result for the divisible sandpile and identify its scaling limit as exactly that of the averaged divisible sandpile. As a corollary, this gives a new quantitative proof of known results on the stabilizability of Abelian sandpiles.