Bernoulli

  • Bernoulli
  • Volume 26, Number 2 (2020), 927-947.

Distances and large deviations in the spatial preferential attachment model

Christian Hirsch and Christian Mönch

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Abstract

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.

Article information

Source
Bernoulli, Volume 26, Number 2 (2020), 927-947.

Dates
Received: September 2018
Revised: January 2019
First available in Project Euclid: 31 January 2020

Permanent link to this document
https://projecteuclid.org/euclid.bj/1580461568

Digital Object Identifier
doi:10.3150/19-BEJ1121

Mathematical Reviews number (MathSciNet)
MR4058356

Zentralblatt MATH identifier
07166552

Keywords
distances large deviation principle Poisson point process preferential attachment

Citation

Hirsch, Christian; Mönch, Christian. Distances and large deviations in the spatial preferential attachment model. Bernoulli 26 (2020), no. 2, 927--947. doi:10.3150/19-BEJ1121. https://projecteuclid.org/euclid.bj/1580461568


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