The half plane UIPT is recurrent

• 成果类型: Article
• 署名作者: Angel, Omer; Ray, Gourab
• 署名单位: University of British Columbia; University of Cambridge
• 刊物名称: PROBABILITY THEORY AND RELATED FIELDS
• ISSN/ISSBN: 0178-8051
• DOI: 10.1007/s00440-017-0767-z
• 发表日期: 2018
• 页码: 657-683
• 关键词: random-walk; triangulations; percolation

摘要

We prove that the half plane version of the uniform infinite planar triangulation (UIPT) is recurrent. The key ingredients of the proof are a construction of a new full plane extension of the half plane UIPT, based on a natural decomposition of the half plane UIPT into independent layers, and an extension of previous methods for proving recurrence of weak local limits (while still using circle packings).