Projects per year
Abstract
We define a class of growing networks in which new nodes are given a spatial position and are connected to existing nodes with a probability mechanism favoring short distances and high degrees. The competition of preferential attachment and spatial clustering gives this model a range of interesting properties. Empirical degree distributions converge to a limit law, which can be a power law with any exponent τ>2 . The average clustering coefficient of the networks converges to a positive limit. Finally, a phase transition occurs in the global clustering coefficients and empirical distribution of edge lengths when the powerlaw exponent crosses the critical value τ=3 . Our main tool in the proof of these results is a general weak law of large numbers in the spirit of Penrose and Yukich.
Original language  English 

Pages (fromto)  632662 
Number of pages  31 
Journal  Annals of Applied Probability 
Volume  25 
Issue number  2 
Early online date  19 Feb 2015 
DOIs  
Publication status  Published  31 Mar 2015 
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Projects
 2 Finished

Emergence of Condensation in Stochastic Systems
Morters, P.
Engineering and Physical Sciences Research Council
1/08/13 → 31/08/16
Project: Research council

INTERSECTION LOCAL TIMES AND STOCHASTIC PROCESSES IN RANDOM MEDIA
Morters, P.
Engineering and Physical Sciences Research Council
1/09/05 → 31/08/10
Project: Research council