Triviality of critical Fortuin-Kasteleyn decorated planar maps for q >4

• 成果类型: Article
• 署名作者: Feng, Yuyang
• 署名单位: University of Chicago
• 刊物名称: PROBABILITY THEORY AND RELATED FIELDS
• ISSN/ISSBN: 0178-8051; 1432-2064
• DOI: 10.1007/s00440-025-01424-2
• 发表日期: 2026-02
• 页码: 299-331
• 关键词: scaling limits; census; MODEL

摘要

We consider infinite random planar maps decorated by the critical Fortuin-Kasteleyn model with parameter q > 4. The paper demonstrates that when appropriately rescaled, these maps converge in law to the infinite continuum random tree as pointed metric-measure spaces, that is, with respect to the local Gromov-Hausdorff-Prokhorov topology. Furthermore, we also show that these maps do not admit any Fortuin-Kasteleyn loops with a macroscopic graph distance diameter. Our proof is based on Scott Sheffield's hamburger-cheeseburger bijection.