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Coletti, Cristian F. [Author]; de Lima, Lucas R. [Author]; Hinsen, Alexander [Author]; Jahnel, Benedikt [Author]; Valesin, Daniel R. [Author]

Limiting shape for first-passage percolation models on random geometric graphs - [published Version]

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  • Media type: Text; Report; E-Book
  • Title: Limiting shape for first-passage percolation models on random geometric graphs
  • Contributor: Coletti, Cristian F. [Author]; de Lima, Lucas R. [Author]; Hinsen, Alexander [Author]; Jahnel, Benedikt [Author]; Valesin, Daniel R. [Author]
  • Published: Berlin : Weierstraß-Institut für Angewandte Analysis und Stochastik, 2021
  • Issue: published Version
  • Language: English
  • DOI: https://doi.org/10.34657/8633; https://doi.org/10.20347/WIAS.PREPRINT.2877
  • ISSN: 2198-5855
  • Keywords: Bernoulli bond percolation ; Poisson--Gilbert graph ; high-density limit ; subergodicity ; isotropic shapes ; Richardson model
  • Origination:
  • Footnote: Diese Datenquelle enthält auch Bestandsnachweise, die nicht zu einem Volltext führen.
  • Description: Let a random geometric graph be defined in the supercritical regime for the existence of a unique infinite connected component in Euclidean space. Consider the first-passage percolation model with independent and identically distributed random variables on the random infinite connected component. We provide sufficient conditions for the existence of the asymptotic shape and we show that the shape is an Euclidean ball. We give some examples exhibiting the result for Bernoulli percolation and the Richardson model. For the Richardson model we further show that it converges weakly to a branching process in the joint limit of large intensities and slow passing times.
  • Access State: Open Access