INTERNAL DLA ON MATED-CRT MAPS

• 成果类型: Article
• 署名作者: Bou-Rabee, Ahmed; Gwynne, Ewain
• 署名单位: New York University; University of Chicago
• 刊物名称: ANNALS OF PROBABILITY
• ISSN/ISSBN: 0091-1798
• DOI: 10.1214/24-AOP1693
• 发表日期: 2024
• 页码: 2173-2237
• 关键词: diffusion-limited aggregation; liouville quantum-gravity; SCALING LIMITS; divisible sandpile; brownian map; fluctuations; CONVERGENCE; percolation; GROWTH; models

摘要

We prove a shape theorem for internal diffusion limited aggregation on mated-CRT maps, a family of random planar maps which approximate Liouville quantum gravity (LQG) surfaces. The limit is a LQG harmonic ball, which we constructed in a companion paper. We also prove an analogous result for the divisible sandpile.