Geodesic stars in random geometry

2021/01/31 by Jean‐François Le Gall, Gall, Jean-François Le
Mathematics · Computer Science · #Point processes and geometric inequalities #Mathematical Dynamics and Fractals #Computational Geometry and Mesh Generation

paper · pdf · doi:10.48550/arxiv.2102.00489

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∈\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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