### Abstract

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

Pages (from-to) | 1989-2021 |

Number of pages | 33 |

Journal | Annals of Applied Probability |

Volume | 20 |

Issue number | 6 |

DOIs | |

Publication status | Published - Dec 2010 |

### Fingerprint

### Keywords

- random graph
- degree distribution
- typed graph
- entropy
- partition function
- random randomly colored graph
- relative entropy
- spins
- Ising model on a random graph
- Erdos-Renyi graph
- joint large deviation principle
- empirical pair measure
- empirical measure

### Cite this

*Annals of Applied Probability*,

*20*(6), 1989-2021. https://doi.org/10.1214/09-AAP647

**Large deviation principles for empirical measures of coloured random graphs.** / Doku-Amponsah, Kwabena; Morters, Peter.

Research output: Contribution to journal › Article

*Annals of Applied Probability*, vol. 20, no. 6, pp. 1989-2021. https://doi.org/10.1214/09-AAP647

}

TY - JOUR

T1 - Large deviation principles for empirical measures of coloured random graphs

AU - Doku-Amponsah, Kwabena

AU - Morters, Peter

PY - 2010/12

Y1 - 2010/12

N2 - For any finite colored graph we define the empirical neighborhood measure, which counts the number of vertices of a given color connected to a given number of vertices of each color, and the empirical pair measure, which counts the number of edges connecting each pair of colors. For a class of models of sparse colored random graphs, we prove large deviation principles for these empirical measures in the weak topology. The rate functions governing our large deviation principles can be expressed explicitly in terms of relative entropies. We derive a large deviation principle for the degree distribution of Erdos-Renyi graphs near criticality.

AB - For any finite colored graph we define the empirical neighborhood measure, which counts the number of vertices of a given color connected to a given number of vertices of each color, and the empirical pair measure, which counts the number of edges connecting each pair of colors. For a class of models of sparse colored random graphs, we prove large deviation principles for these empirical measures in the weak topology. The rate functions governing our large deviation principles can be expressed explicitly in terms of relative entropies. We derive a large deviation principle for the degree distribution of Erdos-Renyi graphs near criticality.

KW - random graph

KW - degree distribution

KW - typed graph

KW - entropy

KW - partition function

KW - random randomly colored graph

KW - relative entropy

KW - spins

KW - Ising model on a random graph

KW - Erdos-Renyi graph

KW - joint large deviation principle

KW - empirical pair measure

KW - empirical measure

UR - http://www.scopus.com/inward/record.url?scp=78650502851&partnerID=8YFLogxK

UR - http://dx.doi.org/10.1214/09-AAP647

U2 - 10.1214/09-AAP647

DO - 10.1214/09-AAP647

M3 - Article

VL - 20

SP - 1989

EP - 2021

JO - Annals of Applied Probability

JF - Annals of Applied Probability

SN - 1050-5164

IS - 6

ER -