### Abstract

We consider first-passage percolation on the configuration model. Once the network has been generated each edge is assigned an i.i.d. weight modeling the passage time of a message along this edge. Then independently two vertices are chosen uniformly at random, a sender and a recipient, and all edges along the geodesic connecting the two vertices are coloured in red (in the case that both vertices are in the same component). In this article we prove local limit theorems for the coloured graph around the recipient in the spirit of Benjamini and Schramm. We consider the explosive regime, in which case the random distances are of finite order, and the Malthusian regime, in which case the random distances are of logarithmic order.

Original language | English |
---|---|

Pages (from-to) | 485–501 |

Number of pages | 17 |

Journal | Journal of Statistical Physics |

Volume | 173 |

Issue number | 3-4 |

Early online date | 7 Apr 2018 |

DOIs | |

Publication status | Published - 19 Nov 2018 |

### Keywords

- Branching processes
- Configuration model
- First passage percolation
- Geodesics
- Local limit
- Random graphs

### ASJC Scopus subject areas

- Statistical and Nonlinear Physics
- Mathematical Physics

## Fingerprint Dive into the research topics of 'Local neighbourhoods for first-passage percolation on the configuration model'. Together they form a unique fingerprint.

## Cite this

Dereich, S., & Ortgiese, M. (2018). Local neighbourhoods for first-passage percolation on the configuration model.

*Journal of Statistical Physics*,*173*(3-4), 485–501. https://doi.org/10.1007/s10955-018-2028-7