Real and complex analysis, 3rd ed.
Real and complex analysis, 3rd ed.
The rank of connection matrices and the dimension of graph algebras
European Journal of Combinatorics
Limits of dense graph sequences
Journal of Combinatorial Theory Series B
Generalized quasirandom graphs
Journal of Combinatorial Theory Series B
Contractors and connectors of graph algebras
Journal of Graph Theory
The missing log in large deviations for triangle counts
Random Structures & Algorithms
The missing log in large deviations for triangle counts
Random Structures & Algorithms
Estimation of exponential random graph models for large social networks via graph limits
Proceedings of the 2013 IEEE/ACM International Conference on Advances in Social Networks Analysis and Mining
| Hi-index | 0.00 |
What does an Erdos-Renyi graph look like when a rare event happens? This paper answers this question when p is fixed and n tends to infinity by establishing a large deviation principle under an appropriate topology. The formulation and proof of the main result uses the recent development of the theory of graph limits by Lovasz and coauthors and Szemeredi's regularity lemma from graph theory. As a basic application of the general principle, we work out large deviations for the number of triangles in G(n,p). Surprisingly, even this simple example yields an interesting double phase transition.