Distances and large deviations in the spatial preferential attachment model

Christian Hirsch; Christian Mönch

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arXiv · 1809.09956

Distances and large deviations in the spatial preferential attachment model

Christian Hirsch·Christian Mönch

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Abstract

We investigate two asymptotic properties of a spatial preferential-attachment model introduced by E. Jacob and P. M\"orters (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.

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Christian Hirsch, Christian Mönch. 2018-09-26. Distances and large deviations in the spatial preferential attachment model. https://arxiv.org/abs/1809.09956

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