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Limits of random trees

Name: Limits of random trees
Creator: Attila Deák
Keywords: Probability (math.PR), FOS: Mathematics, Mathematics - Combinatorics, Combinatorics (math.CO), Mathematics - Probability, 6. Clean water

descriptionPublicationkeyboard_double_arrow_right Article , Preprint , Other literature type 30 Apr 2013Embargo end date: 01 Jan 2014Publisher:Springer Science and Business Media LLCJournal:Acta Mathematica Hungarica, volume 141, pages 185-201 (issn: 0236-5294, eissn: 1588-2632,

Authors: Attila Deák;

doi: 10.1007/s10474-013-0321-0 , 10.48550/arxiv.1401.2521

arXiv: http://arxiv.org/abs/1401.2521

Limits of random trees

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Abstract

Local convergence of bounded degree graphs was introduced by Benjamini and Schramm. This result was extended further by Lyons to bounded average degree graphs. In this paper, we study the convergence of a random tree sequence where the probability of a given tree is proportional to $\prod_{v_i\in V(T)}d(v_i)!$. We show that this sequence is convergent and describe the limit object, which is a random infinite rooted tree.

Related Organizations

Eötvös Loránd University
Hungary

Keywords

Probability (math.PR), FOS: Mathematics, Mathematics - Combinatorics, Combinatorics (math.CO), Mathematics - Probability

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