528 citations
- New York UniversityUS16 papers
- California Institute of TechnologyUS2 papers
- Princeton UniversityUS2 papers
- University of RochesterUS2 papers
- École Normale Supérieure de LyonFR1 paper
- Eindhoven University of TechnologyNL1 paper
- Hong Kong University of Science and TechnologyHK1 paper
- Iowa State UniversityUS1 paper
- Johns Hopkins UniversityUS1 paper
- Lehman CollegeUS1 paper
- Rutgers, The State University of New JerseyUS1 paper
- Sapienza University of RomeIT1 paper
8 papers · 1 filter
A point process describing the component sizes in the critical window of the random graph evolution
Svante Janson, Joel Spencer
We study a point process describing the asymptotic behavior of sizes of the largest components of the random graph G(n,p) in the critical window p=n^{-1}+lambda n^{-4/3}. In partic…
Random walks in a random environment
S R S Varadhan
Random walks as well as diffusions in random media are considered. Methods are developed that allow one to establish large deviation results for both the `quenched' and the `averag…
Cugliandolo-Kurchan equations for dynamics of Spin-Glasses
Gerard Ben Arous, Amir Dembo, Alice Guionnet
We study the Langevin dynamics for the family of spherical -spin disordered mean-field models and prove that in the limit of system size approaching infinity, the empirical…
Coarsening, Nucleation, and the Marked Brownian Web
L. R. G. Fontes, M. Isopi, C. M. Newman +1
Coarsening on a one-dimensional lattice is described by the voter model or equivalently by coalescing (or annihilating) random walks representing the evolving boundaries between re…
A martingale proof of Dobrushin's theorem for non-homogeneous Markov chains
Sunder Sethuraman, S. R. S. Varadhan
In 1956, Dobrushin proved a definitive central limit theorem for non-homogeneous Markov chains. In this note, a shorter and different proof elucidating more the assumptions is give…
Random subgraphs of finite graphs: III. The phase transition for the -cube
Christian Borgs, Jennifer T. Chayes, Remco van der Hofstad +2
We study random subgraphs of the -cube , where nearest-neighbor edges are occupied with probability . Let be the value of for which the expected clust…