### Abstract

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 |

### Fingerprint

### Keywords

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

### ASJC Scopus subject areas

- Statistical and Nonlinear Physics
- Mathematical Physics

### Cite this

*Journal of Statistical Physics*,

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

**Local neighbourhoods for first-passage percolation on the configuration model.** / Dereich, Steffen; Ortgiese, Marcel.

Research output: Contribution to journal › Article

*Journal of Statistical Physics*, vol. 173, no. 3-4, pp. 485–501. https://doi.org/10.1007/s10955-018-2028-7

}

TY - JOUR

T1 - Local neighbourhoods for first-passage percolation on the configuration model

AU - Dereich, Steffen

AU - Ortgiese, Marcel

PY - 2018/11/19

Y1 - 2018/11/19

N2 - 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.

AB - 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.

KW - Branching processes

KW - Configuration model

KW - First passage percolation

KW - Geodesics

KW - Local limit

KW - Random graphs

UR - http://www.scopus.com/inward/record.url?scp=85045041087&partnerID=8YFLogxK

U2 - 10.1007/s10955-018-2028-7

DO - 10.1007/s10955-018-2028-7

M3 - Article

VL - 173

SP - 485

EP - 501

JO - Journal of Statistical Physics

JF - Journal of Statistical Physics

SN - 0022-4715

IS - 3-4

ER -