Using the Schramm-Loewner evolution to explain certain non-local observables in the 2d critical Ising model

Details Using the Schramm-Loewner evolution to explain certain non-local observables in the 2d critical Ising model Using the Schramm-Loewner evolution to explain certain non-local observables in the 2d critical Ising model

2009-05-14

arxiv.org/abs/0905.2430v1

J. Phys. A: Math. Theor., volume 42, number 26, paper 265003, 2009

Physics

Mathematical Physics

v1: 17 pages, 4 figures, to appear in J. Phys. A: Math. Theor.

Scientific paper

10.1088/1751-8113/42/26/265003

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.

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