Geodesics in the Brownian Map: Strong Confluence and Geometric Structure

Jason Miller, Statistical Laboratory, University of Cambridge, United Kingdom. Wei Qian, University of Hong Kong, People's Republic of China, and Univerite Paris-Saclay, Orsay, France

Chapters; 1. Introduction; 2. Preliminaries; 3. Close geodesics must intersect near their endpoints; 4. Finite number of geodesics; 5. Proof of strong confluence and topology of geodesics; 6. Exponent for disjoint geodesics from a point; 7. Completion of proofs of dimension upper bounds; 8. Points connected by 5, 7, and 8 geodesics