1 citations · 1 across the 3 of their papers we have counts for
7 papers
Random walk loop soup
Gregory F. Lawler, José A. Trujillo Ferreras
The Brownian loop soup introduced in Lawler and Werner (2004) is a Poissonian realization from a sigma-finite measure on unrooted loops. This measure satisfies both conformal invar…
The Beurling estimate for a class of random walks
Gregory F. Lawler, Vlada Limic
An estimate of Beurling states that if K is a curve from 0 to the unit circle in the complex plane, then the probability that a Brownian motion starting at -eps reaches the unit ci…
Conformal invariance, universality, and the dimension of the Brownian frontier
Gregory Lawler
This paper describes joint work with Oded Schramm and Wendelin Werner establishing the values of the planar Brownian intersection exponents from which one derives the Hausdorff dim…
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 .
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…