On the continuity of \(\text{SLE}_{\kappa}\) in \(\kappa\)

DOI10.1007/s00440-013-0506-zzbMath1305.60079arXiv1206.1956OpenAlexW2466649013MaRDI QIDQ398767

Steffen Rohde, Carto Wong, Fredrik Johansson Viklund

Publication date: 15 August 2014

Published in: Probability Theory and Related Fields (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1206.1956

zbMATH Keywords

continuity\(\text{SLE}_{\kappa}\)Brownian motion samplesupremum norm

Mathematics Subject Classification ID

Stochastic (Schramm-)Loewner evolution (SLE) (60J67)

Related Items (14)

Convergence of loop-erased random walk in the natural parameterization ⋮ Perturbations of multiple Schramm-Loewner evolution with two non-colliding Dyson Brownian motions ⋮ A support theorem for SLE curves ⋮ An asymptotic radius of convergence for the Loewner equation and simulation of \(\mathrm{SLE}_{\kappa}\) traces via splitting ⋮ A large deviation principle for the Schramm–Loewner evolution in the uniform topology ⋮ A deterministic approach to Loewner-energy minimizers ⋮ The trunks of \(\mathrm{CLE}(4)\) explorations ⋮ Convergence rates for loop-erased random walk and other Loewner curves ⋮ ON THE REGULARITY OF SLE TRACE ⋮ On the existence of SLE trace: finite energy drivers and non-constant \(\kappa \) ⋮ Regularity of SLE in \((t,\kappa)\) and refined GRR estimates ⋮ Continuity in \(\kappa\) in \(\mathrm{SLE}_\kappa\) theory using a constructive method and rough path theory ⋮ Continuity of Zero-Hitting Times of Bessel Processes and Welding Homeomorphisms of SLE$_\kappa$ ⋮ One-dimensional scaling limits in a planar Laplacian random growth model

Cites Work

• Imaginary geometry. I: Interacting SLEs
• Convergence rates for loop-erased random walk and other Loewner curves
• Collisions and spirals of Loewner traces
• Contour lines of the two-dimensional discrete Gaussian free field
• Optimal Hölder exponent for the SLE path
• The dimension of the SLE curves
• Conformal invariance of planar loop-erased random walks and uniform spanning trees.
• Almost sure multifractal spectrum for the tip of an SLE curve
• Hölder regularity and dimension bounds for random curves
• Basic properties of SLE
• Hölder regularity of the SLE trace

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