Using the Schramm-Loewner evolution to explain certain non-local observables in the 2d critical Ising model
Mathematical Physics
2009-06-11 v1 math.MP
Probability
Abstract
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 model at criticality by combining Smirnov's recent proof of the fact that the scaling limit of critical Ising interfaces can be described by chordal SLE(3) with Kozdron and Lawler's configurational measure on mutually avoiding chordal SLE paths. As an extension of this result, we also compute the probability that an SLE(k) path, k in (0,4], and a Brownian motion excursion do not intersect.
Keywords
Cite
@article{arxiv.0905.2430,
title = {Using the Schramm-Loewner evolution to explain certain non-local observables in the 2d critical Ising model},
author = {Michael J. Kozdron},
journal= {arXiv preprint arXiv:0905.2430},
year = {2009}
}
Comments
v1: 17 pages, 4 figures, to appear in J. Phys. A: Math. Theor.