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arXiv · 2105.05615

The volume measure of the Brownian sphere is a Hausdorff measure

Jean-François Le Gall
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Abstract

We prove that the volume measure of the Brownian sphere is equal to a constant multiple of the Hausdorff measure associated with the gauge function $h(r)=r^4\log\log(1/r)$. This shows in particular that the volume measure of the Brownian sphere is determined by its metric structure. As a key ingredient of our proofs, we derive precise estimates on moments of the volume of balls in the Brownian sphere.

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Jean-François Le Gall. 2021-05-12. The volume measure of the Brownian sphere is a Hausdorff measure. https://arxiv.org/abs/2105.05615

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