Electronic Journal of Probability

Escape probability and transience for SLE

Laurence Field and Gregory Lawler

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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.

Article information

Electron. J. Probab., Volume 20 (2015), paper no. 10, 14 pp.

Accepted: 11 February 2015
First available in Project Euclid: 4 June 2016

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Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 60J67: Stochastic (Schramm-)Loewner evolution (SLE)
Secondary: 60J65: Brownian motion [See also 58J65]

Schramm-Loewner evolution Brownian motion

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Field, Laurence; Lawler, Gregory. Escape probability and transience for SLE. Electron. J. Probab. 20 (2015), paper no. 10, 14 pp. doi:10.1214/EJP.v20-3714. https://projecteuclid.org/euclid.ejp/1465067116

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