Bridge Decomposition of Restriction Measures (2009)
Alberts, Tom, Duminil-Copin, Hugo
Motivated by Kesten's bridge decomposition for two-dimensional self-avoiding walks in the upper half plane, we show that the conjectured scaling limit of the half-plane SAW, the SLE(8/3) process,...
The Covariant Measure of SLE on the Boundary (2008)
Alberts, Tom, Sheffield, Scott
We construct a natural measure mu supported on the intersection of a chordal SLE(kappa) curve gamma with the real line R, in the range 4 < kappa < 8. The measure is a function of the SLE path in...
Intersection probabilities for a chordal SLE path and a semicircle (2008)
Alberts, Tom; New York University; Alberts@courant.nyu.edu, Kozdron, Michael J; University Of Regina; Kozdron@stat.math.uregina.ca
We derive a number of estimates for the probability that a chordal SLE path in the upper half plane H intersects a semicircle centred on the real line. We prove that if 0 < κ < 8 and...
Hausdorff Dimension of the SLE Curve Intersected with the Real Line (2008)
Alberts, Tom; Courant Institute Of Mathematical Sciences; Alberts@cims.nyu.edu, Sheffield, Scott; Courant Institute Of Mathematical Sciences; Sheff@cims.nyu.edu
We establish an upper bound on the asymptotic probability of an SLE(kappa) curve hitting two small intervals on the real line as the interval width goes to zero, for the range 4 < kappa < 8. As a...
Hausdorff dimension of the SLE curve intersected with the real line (2007)
Alberts, Tom, Sheffield, Scott
We establish an upper bound on the asymptotic probability of an SLE(kappa) curve hitting two small intervals on the real line as the interval width goes to zero, for the range 4 < kappa < 8. As a...
Intersection probabilities for a chordal SLE path and a semicircle (2007)
Alberts, Tom, Kozdron, Michael J.
We derive a number of estimates for the probability that a chordal SLE path in the upper half plane H intersects a semicircle centred on the real line. We prove that if 0