Home | Contents | Submissions, editors, etc. | Login | Search | EJP
 Electronic Communications in Probability > Vol. 14 (2009) > Paper 29 open journal systems 


Large deviations in randomly coloured random graphs

J. D. Biggins, The University of Sheffield, UK
D.B. Penman, University of Essex, UK


Abstract
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.


Full text: PDF

Pages: 290-301

Published on: July 10, 2009
Bibliography
  1. Biggins, J.D. Large deviations for mixtures. Electron. Comm. Probab., 9 (2004), 60-71. (electronic). MR2081460 (2005k:60082)
  2. Bollobás, Béla. Random graphs. (1985). Academic Press, Inc. [Harcourt Brace Jovanovich, Publishers], London. MR0809996 (87f:05152)
  3. Bollobás, Béla; Janson, Svante; Riordan, Oliver. The phase transition in inhomogeneous random graphs. Random Structures Algorithms 31 (2007), 3-122. MR2337396 (2008e:05124)
  4. Cannings, C; Penman, D.B. Models of random graphs and their applications. Stochastic processes: modelling and simulation, Handbook of Statist., 21, (2003), 51-91. North-Holland, Amsterdam MR1973541 (2004c:05181)
  5. Cerquetti, Annalisa; Fortini, Sandra. A Poisson approximation for coloured graphs under exchangeability. Sankhya 68 (2006), 183-197. MR2303080 (2007m:60056)
  6. Chaganty, Narasinga R. Large deviations for joint distributions and statistical applications. Sankhya Ser. A 59 (1997), 147-166. MR1665683 (2000b:60067)
  7. Dembo, Amir; Zeitouni, Ofer. Large deviations techniques and applications. Jones and Bartlett Publishers, Boston, MA, (1993) MR1202429 (95a:60034)
  8. Dinwoodie, I. H.; Zabell, S. L. Large deviations for exchangeable random vectors. Ann. Probab. 20 (1992), 1147-1166. MR1175254 (93g:60059)
  9. Doku-Amponsah, Kwabena; Mörters, Peter. Large deviation principles for empirical measures of coloured random graphs. arXiv:math/0607545v1 (2006).
  10. Penman. D.B. Random graphs with correlation structure. Ph.D thesis, University of Sheffield, (1998).
  11. Rockafellar, R. Tyrrell. Convex analysis. Princeton Mathematical Series, 28. Princeton University Press, Princeton, N.J. (1970) MR0274683 (43 #445)
















Research
Support Tool
Capture Cite
View Metadata
Printer Friendly
Context
Author Address
Action
Email Author
Email Others


Home | Contents | Submissions, editors, etc. | Login | Search | EJP

Electronic Communications in Probability. ISSN: 1083-589X