Limiting shape for First-Passage Percolation models on Random Geometric Graphs
| Autor: | Cristian F. Coletti, Lucas R. de Lima, Alexander Hinsen, Benedikt Jahnel, Daniel Valesin |
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| Rok vydání: | 2021 |
| Předmět: |
Statistics and Probability
isotropic shapes General Mathematics Probability (math.PR) 52A22 Richardson model high-density limit subergodicity Poisson--Gilbert graph 60K35 FOS: Mathematics Primary: 52A22 60F15 Secondary: 60K35 Bernoulli bond percolation 60F15 Statistics Probability and Uncertainty Mathematics - Probability |
| DOI: | 10.48550/arxiv.2109.07813 |
| Popis: | 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 nonstandard branching process in the joint limit of large intensities and slow passage times. Comment: 23 pages, 3 figures. The references were upadted in the latest versions and typographical errors corrected |
| Databáze: | OpenAIRE |
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