THE WIRED MINIMAL SPANNING FOREST ON THEPOISSON-WEIGHTED INFINITE TREE

• 成果类型: Article
• 署名作者: Nachmias, Asaf; Tang, Pengfei
• 署名单位: Tel Aviv University; Tianjin University
• 刊物名称: ANNALS OF APPLIED PROBABILITY
• ISSN/ISSBN: 1050-5164
• DOI: 10.1214/23-AAP2027
• 发表日期: 2024
• 页码: 2415-2446
• 关键词: random-walk; percolation; cluster

摘要

We study the spectral and diffusive properties of the wired minimal span-ning forest (WMSF) on the Poisson-weighted infinite tree (PWIT). LetMbethe tree containing the root in the WMSF on the PWIT and(Y-n)(n >= 0)be asimple random walk onMstarting from the root. We show that almost surelyMhasP[Y-2n=Y-0]=n-(3/4+o(1))and dist(Y-0,Y-n)=n(1/4+o(1))with highprobability. That is, the spectral dimension ofMis 3/2 and its typical dis-placement exponent is 1/4, almost surely. These confirm Addario-Berry'spredictions (Addario-Berry (2013)).