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2009 Large deviations in randomly coloured random graphs
J. D. Biggins, D.B. Penman
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Electron. Commun. Probab. 14: 290-301 (2009). DOI: 10.1214/ECP.v14-1478


Models of random graphs are considered where the presence or absence of an edge depends on the random types (colours) of its vertices, so that whether or not edges are present can be dependent. The principal objective is to study large deviations in the number of edges. These graphs provide a natural example with two different non-degenerate large deviation regimes, one arising from large deviations in the colourings followed by typical edge placement and the other from large deviation in edge placement. A secondary objective is to illustrate the use of a general result on large deviations for mixtures.


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J. D. Biggins. D.B. Penman. "Large deviations in randomly coloured random graphs." Electron. Commun. Probab. 14 290 - 301, 2009.


Accepted: 10 July 2009; Published: 2009
First available in Project Euclid: 6 June 2016

zbMATH: 1185.05125
MathSciNet: MR2524980
Digital Object Identifier: 10.1214/ECP.v14-1478

Primary: 05C80
Secondary: 60F10

Keywords: large deviations , mixture , Random graphs , Rate function


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