Quenched and averaged tails of the heat kernel of the two-dimensional uniform spanning tree

• 成果类型: Article
• 署名作者: Barlow, M. T.; Croydon, D. A.; Kumagai, T.
• 署名单位: University of British Columbia; Kyoto University
• 刊物名称: PROBABILITY THEORY AND RELATED FIELDS
• ISSN/ISSBN: 0178-8051
• DOI: 10.1007/s00440-021-01078-w
• 发表日期: 2021
• 页码: 57-111
• 关键词: incipient infinite cluster; erased random-walks; SCALING LIMITS; Invariance

摘要

This article investigates the heat kernel of the two-dimensional uniform spanning tree. We improve previous work by demonstrating the occurrence of log-logarithmic fluctuations around the leading order polynomial behaviour for the on-diagonal part of the quenched heat kernel. In addition we give two-sided estimates for the averaged heat kernel, and we show that the exponents that appear in the off-diagonal parts of the quenched and averaged versions of the heat kernel differ. Finally, we derive various scaling limits for the heat kernel, the implications of which include enabling us to sharpen the known asymptotics regarding the on-diagonal part of the averaged heat kernel and the expected distance travelled by the associated simple random walk.