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Random Graphs
  • 1,993
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The phase transition in inhomogeneous random graphs
The “classical” random graph models, in particular G(n,p), are “homogeneous,” in the sense that the degrees (for example) tend to be concentrated around a typical value. Many graphs arising in theExpand
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Poisson Approximation
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Functional limit theorems for multitype branching processes and generalized Pólya urns
A functional limit theorem is proved for multitype continuous time Markov branching processes. As consequences, we obtain limit theorems for the branching process stopped by some stopping rule, forExpand
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Gaussian Hilbert Spaces
1. Gaussian Hilbert spaces 2. Wiener chaos 3. Wick products 4. Tensor products and Fock spaces 5. Hypercontractivity 6. Distributions of variables with finite chaos expansions 7. StochasticExpand
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The phase transition in inhomogeneous random graphs
We introduce a very general model of an inhomogenous random graph with independence between the edges, which scales so that the number of edges is linear in the number of vertices. This scalingExpand
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The Birth of the Giant Component
Limiting distributions are derived for the sparse connected components that are present when a random graph on n vertices has approximately 1/2n edges. In particular, we show that such a graphExpand
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Random graphs
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Limit theorems for triangular urn schemes
Abstract.We study a generalized Pólya urn with balls of two colours and a triangular replacement matrix; the urn is not required to be balanced. We prove limit theorems describing the asymptoticExpand
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