22 citations · 22 across the 3 of their papers we have counts for
5 papers · 1 filter
On the scaling limit of planar self-avoiding walk
Gregory F. Lawler, Oded Schramm, Wendelin Werner
A planar self-avoiding walk (SAW) is a nearest neighbor random walk path in the square lattice with no self-intersection. A planar self-avoiding polygon (SAP) is a loop with no sel…
One-arm exponent for critical 2D percolation
Gregory F. Lawler, Oded Schramm, Wendelin Werner
The probability that the cluster of the origin in critical site percolation on the triangular grid has diameter larger than is proved to decay like as .
A percolation formula
Oded Schramm
Let be an arc on the boundary of the unit disk . We prove an asymptotic formula for the probability that there is a percolation cluster for critical site percolation on…
Sharp estimates for Brownian non-intersection probabilities
Greg Lawler, Oded Schramm, Wendelin Werner
This paper gives an accessible (but still technical) self-contained proof to the fact that the intersection probabilities for planar Brownian motion are given in terms of the inter…
Percolation Perturbations in Potential Theory and Random Walks
Itai Benjamini, Russell Lyons, Oded Schramm
We show that on a Cayley graph of a nonamenable group, almost surely the infinite clusters of Bernoulli percolation are transient for simple random walk, that simple random walk on…