文章基本信息

标题：Uniform spanning trees on Sierpiński graphs
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作者：Masato Shinoda ; Elmar Teufl ; Stephan Wagner 等
期刊名称：Latin American Journal of Probability and Mathematical Statistics
电子版ISSN：1980-0436
出版年度：2014
卷号：XI
页码：737-780
出版社：Instituto Nacional De Matemática Pura E Aplicada
摘要：We study spanning trees on Sierpinski graphs (i.e., nite approximationsto the Sierpinski gasket) that are chosen uniformly at random. We constructa joint probability space for uniform spanning trees on every nite Sierpinski graphand show that this construction gives rise to a multi-type Galton-Watson tree. Wederive a number of structural results, for instance on the degree distribution. Theconnection between uniform spanning trees and loop-erased random walk is thenexploited to prove convergence of the latter to a continuous stochastic process.Some geometric properties of this limit process, such as the Hausdor dimension,are investigated as well. The method is also applicable to other self-similar graphswith a sucient degree of symmetry.
关键词：niform spanning trees; Sierpinski graphs; loop-erased random walk;limit behaviour.