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The regularity of SLE

Yizheng Yuan (Cambridge University)
Yizheng Yuan (Cambridge University)
When Aug 08, 2023
from 04:00 PM to 05:00 PM
Where Online via Zoom
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Abstract: I will present a quick introduction to SLE (Schramm-Loewner evolution), an important object appearing in random planar geometry and statistical physics. It describes a family of random fractal curves that exhibit conformal symmetries which underlie their prominence. Natural questions for fractal curves include their Hölder and p-variation exponents. I will explain how to find these and how to go further into finding the exact regularities (i.e. the correct logarithmic refinements). An important notion in the analysis is the "natural length" of the SLE curves. Our results (obtained jointly with Nina Holden) imply some important properties of this natural length, including a new characterisation.

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