Minkowski content and natural parameterization for the Schramm-Loewner evolution
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Publication:2352749
DOI10.1214/13-AOP874zbMath1331.60165arXiv1211.4146OpenAlexW3104479128MaRDI QIDQ2352749
Mohammad A. Rezaei, Gregory F. Lawler
Publication date: 6 July 2015
Published in: The Annals of Probability (Search for Journal in Brave)
Full work available at URL: https://arxiv.org/abs/1211.4146
Interacting random processes; statistical mechanics type models; percolation theory (60K35) Critical phenomena in equilibrium statistical mechanics (82B27) Stochastic (Schramm-)Loewner evolution (SLE) (60J67)
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Cites Work
- Unnamed Item
- Multi-point Green's functions for SLE and an estimate of Beffara
- SLE curves and natural parametrization
- Conformal invariance in random cluster models. I: Holomorphic fermions in the Ising model
- Optimal Hölder exponent for the SLE path
- A natural parametrization for the Schramm-Loewner evolution
- Hausdorff measure of SLE curves
- The dimension of the SLE curves
- Intersection probabilities for a chordal SLE path and a semicircle
- Scaling limits of loop-erased random walks and uniform spanning trees
- Conformal invariance of planar loop-erased random walks and uniform spanning trees.
- Harmonic explorer and its convergence to \(\text{SLE}_4\)
- Critical percolation in the plane: conformal invariance, Cardy's formula, scaling limits
- Continuity of Radial and Two-Sided Radial 𝑆𝐿𝐸 at the Terminal Point
- Hölder regularity of the SLE trace