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Random Graphs
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
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
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
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
The Birth of the Giant Component
A “uniform” model of random graphs, which allows self-loops and multiple edges, is shown to lead to formulas that are substanitially simpler than the analogous formulas for the classical random graphs of Erdos and Renyi. Expand
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
Random Regular Graphs: Asymptotic Distributions and Contiguity
  • S. Janson
  • Mathematics, Computer Science
  • Comb. Probab. Comput.
  • 1 December 1995
The asymptotic distribution of the number of Hamilton cycles in a random regular graph is determined, and results imply that some different models of random regular graphs are contiguous, which means that they are qualitatively asymPTotically equivalent. Expand
Large deviations for sums of partly dependent random variables
We use and extend a method by Hoeffding to obtain strong large deviation bounds for sums of dependent random variables with suitable dependency structure. The method is based on breaking up the sumExpand