Schramm-Loewner Equations Driven by Symmetric Stable Processes

Abstract

We consider shape, size and regularity of the hulls of the chordal Schramm-Loewner evolution driven by a symmetric alpha-stable process. We obtain derivative estimates, show that the complements of the hulls are Hoelder domains, prove that the hulls have Hausdorff dimension 1, and show that the trace is right-continuous with left limits almost surely.

22 pages, 4 figures

References in corpus (3)

• Stochastic Loewner evolution driven by Levy processes
• SLE and alpha-SLE driven by Levy processes
• Cadlag curves of SLE driven by Levy processes

Cited by in corpus (8)

• On Harmonic Measure of the Whole Plane Levy-Loewner Evolution
• The Coefficient Problem and Multifractality of Whole-Plane SLE and LLE
• q-deformed Loewner evolution
• Cadlag curves of SLE driven by Levy processes
• Refined regularity of SLE
• Effect of Random Time Changes on Loewner Hulls
• On Loewner chains driven by semimartingales and complex Bessel-type SDEs
• Rescaled Levy-Loewner hulls and random growth