Distances and large deviations in the spatial preferential attachment model

Abstract

We investigate two asymptotic properties of a spatial preferential-attachment model introduced by E. Jacob and P. Mörters (2013). First, in a regime of strong linear reinforcement, we show that typical distances are at most of doubly-logarithmic order. Second, we derive a large deviation principle for the empirical neighbourhood structure and express the rate function as solution to an entropy minimisation problem in the space of stationary marked point processes.

arXiv comment19 pages, 1 figure