VOL. 87 | 2021 The number of spanning clusters of the uniform spanning tree in three dimensions
Chapter Author(s) Omer Angel, David A. Croydon, Sarai Hernandez-Torres, Daisuke Shiraishi
Editor(s) Yuzuru Inahama, Hirofumi Osada, Tomoyuki Shirai
Adv. Stud. Pure Math., 2021: 403-414 (2021) DOI: 10.2969/aspm/08710403

Abstract

Let Uδ be the uniform spanning tree on δZ3. A spanning cluster of Uδ is a connected component of the restriction of Uδ to the unit cube [0,1]3 that connects the left face {0}×[0,1]2 to the right face {1}×[0,1]2. In this note, we will prove that the number of the spanning clusters is tight as δ0, which resolves an open question raised by Benjamini in [4].

Information

Published: 1 January 2021
First available in Project Euclid: 20 January 2022

Digital Object Identifier: 10.2969/aspm/08710403

Subjects:
Primary: 60D05
Secondary: 05C80

Keywords: spanning clusters , Uniform spanning tree

Rights: Copyright © 2021 Mathematical Society of Japan

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