Open Access
May 2020 Distances and large deviations in the spatial preferential attachment model
Christian Hirsch, Christian Mönch
Bernoulli 26(2): 927-947 (May 2020). DOI: 10.3150/19-BEJ1121


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.


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Christian Hirsch. Christian Mönch. "Distances and large deviations in the spatial preferential attachment model." Bernoulli 26 (2) 927 - 947, May 2020.


Received: 1 September 2018; Revised: 1 January 2019; Published: May 2020
First available in Project Euclid: 31 January 2020

zbMATH: 07166552
MathSciNet: MR4058356
Digital Object Identifier: 10.3150/19-BEJ1121

Keywords: distances , large deviation principle , Poisson point process , preferential attachment

Rights: Copyright © 2020 Bernoulli Society for Mathematical Statistics and Probability

Vol.26 • No. 2 • May 2020
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