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 , we prove that the set of all geodesic stars with m arms in the Brownian sphere has dimension . This complements recent results of Miller and Qian, who proved that this dimension is smaller than or equal to .
The present work was supported by the ERC Advanced Grant 740943 GEOBROWN.
I thank Jason Miller and Wei Qian for keeping me informed of their ongoing work. I am also indebted to the referee for a careful reading of the manuscript and several useful remarks.
"Geodesic stars in random geometry." Ann. Probab. 50 (3) 1013 - 1058, May 2022. https://doi.org/10.1214/21-AOP1553