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7 papers · 2 filters
The Full Brownian Web as Scaling Limit of Stochastic Flows
Luiz Renato Fontes, Charles M. Newman
In this paper we construct an object which we call the full Brownian web (FBW) and prove that the collection of all space-time trajectories of a class of one-dimensional stochastic…
Random-Turn Hex and other selection games
Yuval Peres, Oded Schramm, Scott Sheffield +1
The game of Hex has two players who take turns placing stones of their respective colors on the hexagons of a rhombus-shaped hexagonal grid. Black wins by completing a crossing bet…
A large deviation inequality for vector functions on finite reversible Markov Chains
Vladislav Kargin
Let be the sum of vector-valued functions defined on a finite Markov chain. An analogue of the Bernstein--Hoeffding inequality is derived for the probability of large deviati…
Euler integrals for commuting SLEs
Julien Dubedat
Schramm-Loewner Evolutions (SLEs) have proved an efficient way to describe a single continuous random conformally invariant interface in a simply-connected planar domain; the admis…
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…