Percolation on random triangulations and stable looptrees

• 成果类型: Article
• 署名作者: Curien, Nicolas; Kortchemski, Igor
• 署名单位: Centre National de la Recherche Scientifique (CNRS); Sorbonne Universite; Sorbonne Universite; Universite PSL; Ecole Normale Superieure (ENS)
• 刊物名称: PROBABILITY THEORY AND RELATED FIELDS
• ISSN/ISSBN: 0178-8051
• DOI: 10.1007/s00440-014-0593-5
• 发表日期: 2015
• 页码: 303-337
• 关键词: trees; limit; THEOREM; GROWTH

摘要

We study site percolation on Angel and Schramm's uniform infinite planar triangulation. We compute several critical and near-critical exponents, and describe the scaling limit of the boundary of large percolation clusters in all regimes (subcritical, critical and supercritical). We prove in particular that the scaling limit of the boundary of large critical percolation clusters is the random stable looptree of index , which was introduced in Curien and Kortchemski (Random stable looptrees. arXiv:1304.1044, 2014). We also give a conjecture linking looptrees of any index with scaling limits of cluster boundaries in random triangulations decorated with models.