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- Publications
- Influence

The phase transition in inhomogeneous random graphs

- B. Bollobás, S. Janson, O. Riordan
- Mathematics
- 1 August 2007

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 the… Expand

Functional limit theorems for multitype branching processes and generalized Pólya urns

- S. Janson
- Mathematics
- 1 April 2004

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, for… Expand

Gaussian Hilbert Spaces

- S. Janson
- Mathematics
- 13 July 1997

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. Stochastic… Expand

The phase transition in inhomogeneous random graphs

- B. Bollobás, S. Janson, O. Riordan
- Mathematics, Computer Science
- Random Struct. Algorithms
- 29 April 2005

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 scaling… Expand

The Birth of the Giant Component

- S. Janson, D. Knuth, T. Luczak, B. Pittel
- Computer Science, Mathematics
- Random Struct. Algorithms
- 1 October 1993

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 graph… Expand

Random graphs

- S. Janson, T. Luczak, A. Rucinski
- Computer Science
- Wiley-Interscience series in discrete mathematics…
- 28 February 2000

Mean oscillation and commutators of singular integral operators

- S. Janson
- Mathematics
- 1 December 1978

Limit theorems for triangular urn schemes

- S. Janson
- Mathematics
- 1 March 2006

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 asymptotic… Expand