STABLE SHREDDED SPHERES AND CAUSAL RANDOM MAPS WITH LARGE FACES

• 成果类型: Article
• 署名作者: Bjornberg, Jakob; Curien, Nicolas; Stefansson, Sigurdur Orn
• 署名单位: Chalmers University of Technology; University of Gothenburg; Universite Paris Saclay; Institut Universitaire de France; University of Iceland
• 刊物名称: ANNALS OF PROBABILITY
• ISSN/ISSBN: 0091-1798
• DOI: 10.1214/22-AOP1579
• 发表日期: 2022
• 页码: 2056-2084
• 关键词: scaling limits; planar maps; THEOREM; contour; trees

摘要

We introduce a new familiy of random compact metric spaces S-alpha for alpha is an element of (1, 2), which we call stable shredded spheres. They are constructed from excursions of alpha-stable Levy processes on [0, 1] possessing no negative jumps. Informally, viewing the graph of the Levy excursion in the plane, each jump of the process is cut open and replaced by a circle, and then all points on the graph at equal height, which are not separated by a jump, are identified. We show that the shredded spheres arise as scaling limits of models of causal random planar maps with large faces introduced by Di Francesco and Guitter. We also establish that their Hausdorff dimension is almost surely equal to alpha. Point identification in the shredded spheres is intimately connected to the presence of decrease points in stable spectrally positive Levy processes, as studied by Bertoin in the 1990s.