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arXiv · 2102.00489

Geodesic stars in random geometry

Jean-François Le Gall
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Abstract

A point of a metric space is called a geodesic star with $m$ arms if it is the endpoint of $m$ disjoint geodesics. For every $m\in\{1,2,3,4\}$, we prove that the set of all geodesic stars with $m$ arms in the Brownian sphere has dimension $5-m$. This complements recent results of Miller and Qian, who proved that this dimension is smaller than or equal to $5-m$.

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Jean-François Le Gall. 2021-01-31. Geodesic stars in random geometry. https://arxiv.org/abs/2102.00489

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