Invariant random graphs with iid degrees in a general geography
type: Item
instance of: scholarly article
title: Invariant random graphs with iid degrees in a general geography
zbMATH Open document ID: 1170.05055
author: Johan Jonasson
publication date: 2009-05-13T00:00:00Z
review text: Let \(G\) be an infinite transitive finite-degree graph specifying the space geography into which an automorphism-invariant random graph with specified degree distribution should be defined. The existence of such random graphs is investigated when \(G\) has polynomial, exponential, or intermediate growth rate. Conditions are given on the expected edge lengths and on the degree distribution. Special cases of \(G\) considered are integer lattices and regular trees of degree three or more. More exotic geographies include the Trofimov graph, the Diestel-Leader graphs, and the Grigorchuk group.
Mathematics Subject Classification ID: 05C80
Mathematics Subject Classification ID: 05C07
Mathematics Subject Classification ID: 60G10
Mathematics Subject Classification ID: 60B05
Mathematics Subject Classification ID: 60K99
Mathematics Subject Classification ID: 60B15
zbMATH DE Number: 5553446
zbMATH Keywords: random graph
zbMATH Keywords: degree distribution
zbMATH Keywords: automorphism
zbMATH Keywords: growth rate
MaRDI profile type: Publication
full work available at URL: s00440-008-0160-z
OpenAlex ID: W2137494627
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DOI: 10.1007/S00440-008-0160-Z
published in: Zeitschrift für Wahrscheinlichkeitstheorie und Verwandte Gebiete
description: scientific article; zbMATH DE number 5553446