### Distances in large random regular networks

**Salez, J ***(Université Paris 7 - Denis-Diderot)*

Thursday 15 August 2013, 11:00-11:45

Seminar Room 1, Newton Institute

#### Abstract

We study the array of point-to-point distances in large random regular graphs equipped with exponential edge-lengths. The asymptotic marginal distribution of a single entry is now well-understood, thanks to the work of Bhamidi, van der Hofstad and Hooghiemstra (2010). In this talk, we will show that the whole array, suitably recentered, converges in the weak sense to a rather simple infinite random array. This confirms a prediction of David Aldous.

#### Presentation

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