Escape probability and transience for SLE

Abstract

We give estimates for the probability that a chordal, radial or two-sided radial SLE${}_{\kappa }$ curve retreats far from its terminal point after coming close to it, for $\kappa \le 4$. The estimates are uniform over all initial segments of the curve, and are sharp up to a universal constant.

20 pages, 4 figures

References in corpus (3)

• Minkowski content and natural parameterization for the Schramm-Loewner evolution
• Multi-point Green's functions for SLE and an estimate of Beffara
• Continuity of radial and two-sided radial $SL{E}_{\kappa }$ at the terminal point

Cited by in corpus (6)

• Convergence of radial loop-erased random walk in the natural parametrization
• Large deviations of multichordal SLE${}_{0+}$, real rational functions, and zeta-regularized determinants of Laplacians
• Two-sided radial SLE and length-biased chordal SLE
• Refined regularity of SLE
• Regularity of the Schramm-Loewner evolution: Up-to-constant variation and modulus of continuity
• Multi-arm incipient infinite clusters in 2D: scaling limits and winding numbers