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September 2013 Joint distribution of distances in large random regular networks
Justin Salez
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J. Appl. Probab. 50(3): 861-870 (September 2013). DOI: 10.1239/jap/1378401241

Abstract

We study the array of point-to-point distances in random regular graphs equipped with exponential edge lengths. We consider the regime where the degree is kept fixed while the number of vertices tends to ∞. The marginal distribution of an individual entry is now well understood, thanks to the work of Bhamidi, van der Hofstad and Hooghiemstra (2010). The purpose of this note is to show that the whole array, suitably recentered, converges in the weak sense to an explicit infinite random array. Our proof consists in analyzing the invasion of the network by several mutually exclusive flows emanating from different sources and propagating simultaneously along the edges.

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Justin Salez. "Joint distribution of distances in large random regular networks." J. Appl. Probab. 50 (3) 861 - 870, September 2013. https://doi.org/10.1239/jap/1378401241

Information

Published: September 2013
First available in Project Euclid: 5 September 2013

zbMATH: 1277.60021
MathSciNet: MR3102519
Digital Object Identifier: 10.1239/jap/1378401241

Subjects:
Primary: 60C05
Secondary: 05C80 , 90B15

Keywords: branching process approximation , configuration model , distance matrix , first passage percolation , multitype Richardson process , random regular graph

Rights: Copyright © 2013 Applied Probability Trust

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Vol.50 • No. 3 • September 2013
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