374 citations · 1.8k across the 64 of their papers we have counts for
7 papers · 2 filters
Conformal invariance of planar loop-erased random walks and uniform spanning trees
Gregory F. Lawler, Oded Schramm, Wendelin Werner
We prove that the scaling limit of loop-erased random walk in a simply connected domain is equal to the radial SLE(2) path in . In particular, the limit exists and is confor…
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…
Geometry of the Uniform Spanning Forest: Transitions in Dimensions 4, 8, 12
Itai Benjamini, Harry Kesten, Yuval Peres +1
The uniform spanning forest (USF) in Z^d is the weak limit of random, uniformly chosen, spanning trees in [-n,n]^d. Pemantle proved that the USF consists a.s. of a single tree if a…
Markov Chain Intersections and the Loop-Erased Walk
Russell Lyons, Yuval Peres, Oded Schramm
Let X and Y be independent transient Markov chains on the same state space that have the same transition probabilities. Let L denote the ``loop-erased path'' obtained from the path…
Basic properties of SLE
Steffen Rohde, Oded Schramm
SLE is a random growth process based on Loewner's equation with driving parameter a one-dimensional Brownian motion running with speed . This process is intimately connected wit…