# Large deviation principles for empirical measures of coloured random graphs

### Reference:

Doku-Amponsah, K. and Morters, P., 2010. Large deviation principles for empirical measures of coloured random graphs. *Annals of Applied Probability*, 20 (6), pp. 1989-2021.

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### Official URL:

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

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### Abstract

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.

### Details

Item Type | Articles | ||||

Creators | Doku-Amponsah, K.and Morters, P. | ||||

DOI | 10.1214/09-AAP647 | ||||

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Uncontrolled 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 | ||||

Departments | Faculty of Science > Mathematical Sciences | ||||

Research Centres | Centre for Mathematical Biology | ||||

Refereed | Yes | ||||

Status | Published | ||||

ID Code | 16678 |

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