Limits of the boundary of random planar maps

• 成果类型: Article
• 署名作者: Richier, Loic
• 署名单位: Institut Polytechnique de Paris; Ecole Polytechnique
• 刊物名称: PROBABILITY THEORY AND RELATED FIELDS
• ISSN/ISSBN: 0178-8051
• DOI: 10.1007/s00440-017-0820-y
• 发表日期: 2018
• 页码: 789-827
• 关键词: scaling limits; random-walk; trees

摘要

We discuss asymptotics for the boundary of critical Boltzmann planar maps under the assumption that the distribution of the degree of a typical face is in the domain of attraction of a stable distribution with parameter it has a component homeomorphic to the half-plane. As an application, we identify the limits of loops conditioned to be large in the rigid loop model on quadrangulations, proving thereby a conjecture of Curien and Kortchemski.