Natural spanning trees of \({\mathbb{Z}}^ d\) are recurrent
type: Item
instance of: scholarly article
title: Natural spanning trees of \({\mathbb{Z}}^ d\) are recurrent
zbMATH Open document ID: 0599.05018
DOI: 10.1016/0012-365X(86)90107-X
author: Peter Gerl
published in: Discrete Mathematics
publication date: 1986-01-01T00:00:00Z
review text: An old result of Polya states that the simple random walk on \({\mathbb{Z}}^ d\) is recurrent for \(d=1\) and 2, but transient for \(d\geq 3\). In the present paper it is shown that the natural spanning tree of \({\mathbb{Z}}^ d\) is recurrent for every \(d=1,2,3,... \). An asymptotic result on the probability of returning to the origin in n steps is proved by the method of Darboux.
reviewed by: Peter Kirschenhofer
Mathematics Subject Classification ID: 05C05
Mathematics Subject Classification ID: 60G50
zbMATH DE Number: 3966095
zbMATH Keywords: spanning tree
zbMATH Keywords: recurrence
zbMATH Keywords: random walk
MaRDI profile type: Publication
cites work: Asymptotic Methods in Enumeration
cites work: Recurrent and transient trees
cites work: Q5635252
cites work: Q3706275
cites work: Q5731217
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description: scientific article; zbMATH DE number 3966095