On Exact Multi-fractal Spectrum of the Whole-Plane SLE
Igor Loutsenko, Oksana Yermolayeva
TL;DR
This paper derives the exact multi-fractal spectrum of the whole-plane SLE by solving fundamental equations for the moments of conformal map derivatives, providing precise insights into its fractal properties.
Contribution
It presents the first exact calculation of the average integral means beta-spectrum for the whole-plane SLE.
Findings
Exact multi-fractal spectrum obtained for the whole-plane SLE.
Analytical solutions for moments of conformal map derivatives.
Enhanced understanding of the fractal geometry of SLE paths.
Abstract
We consider the whole-plane Shramm-Loewner evolution. Using exact solutions of fundamental equations for moments of derivative of conformal mappings we determine its average integral means beta-spectrum.
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