On the rate of convergence of loop-erased random walk to SLE(2) (2009)
Benes, Christian, Johansson, Fredrik, Kozdron, Michael J.
We derive a rate of convergence of the Loewner driving function for loop-erased random walk to Brownian motion with speed 2 on the unit circle, the Loewner driving function for radial SLE(2).
We present a mathematical proof of theoretical predictions made by Arguin and Saint-Aubin, as well as by Bauer, Bernard, and Kytola, about certain non-local observables for the two-dimensional Ising...
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...
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
The scaling limit of Fomin's identity for two paths in the plane (2007)
We review some recently completed research that establishes the scaling limit of Fomin's identity for loop-erased random walk on Z^2 in terms of the chordal Schramm-Loewner evolution (SLE) with...
The configurational measure on mutually avoiding SLE paths (2006)
Kozdron, Michael J., Lawler, Gregory F.
We define multiple chordal SLEs in a simply connected domain by considering a natural configurational measure on paths. We show how to construct these measures so that they are conformally covariant...
Estimates of Random Walk Exit Probabilities and Application to Loop-Erased Random Walk (2005)
Kozdron, Michael J.; University Of Regina, Canada; Kozdron@math.uregina.ca, Lawler, Gregory F.; Cornell University, USA; Lawler@math.cornell.edu
We prove an estimate for the probability that a simple random walk in a simply connected subset A of Z2 starting on the boundary exits A at another specified boundary point. The estimates are uniform...
On the scaling limit of simple random walk excursion measure in the plane (2005)
The Brownian excursion measure is a conformally invariant infinite measure on curves. It figured prominently in one of the first major applications of SLE, namely the explicit calculations of the...
Estimates of random walk exit probabilities and application to loop-erased random walk (2005)
Kozdron, Michael J., Lawler, Gregory F.
We prove an estimate for the probability that a simple random walk in a simply connected subset A of Z^2 starting on the boundary exits A at another specified boundary point. The estimates are...