This paper considers two asymptotic properties of a spatial preferential-attachment model introduced by E. Jacob and P. Mörters (In Algorithms and Models for the Web Graph (2013) 14–25 Springer). 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.
"Distances and large deviations in the spatial preferential attachment model." Bernoulli 26 (2) 927 - 947, May 2020. https://doi.org/10.3150/19-BEJ1121