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Minkowski content and exceptional sets for Brownian paths

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Minkowski content and exceptional sets for Brownian paths
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11
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CC Attribution - NonCommercial - NoDerivatives 4.0 International:
You are free to use, copy, distribute and transmit the work or content in unchanged form for any legal and non-commercial purpose as long as the work is attributed to the author in the manner specified by the author or licensor.
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Release Date2017
LanguageEnglish

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Abstract
Hausdorff measure is often used to measure fractal sets. However, there is a more natural quantity, Minkowski content, which more closely matches the scaling limit of discrete counting measures and is closely related to the idea of local time. I will discuss this in the context of several sets for which Chris Burdzy made fundamental contributions: cut points for Brownian paths and outer boundary of two-dimensional Brownian motion. The latter is closely related to the Schramm-Loewner evolution (SLE). I will include joint work with Mohammad Rezaei and recent work with Nina Holden, Xinyi Li, and Xin Sun.
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