2023/02/02 by Jean‐François Le Gall, Gall, Jean-François Le, Armand Riera +1
Biochemistry, Genetics and Molecular Biology · Mathematics · #05C80 #60D05 #Diffusion and Search Dynamics #FOS: Mathematics #Point processes and geometric inequalities #Probability (math.PR) #Stochastic processes and statistical mechanics
paper · pdf · doi:10.48550/arxiv.2302.01138
openalex publication_date 2023/02/02 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We derive a new representation of the Brownian disk in terms of a forest of labeled trees, where labels correspond to distances from a subset of the boundary. We then use this representation to obtain a spatial Markov property showing that the complement of a hull centered at a boundary point of a Brownian disk is again a Brownian disk, with a random perimeter, and is independent of the hull conditionally on its perimeter. Our proofs rely in part on a study of the peeling process for triangulations with a boundary, which is of independent interest. The results of the present work will be applied to a continuous version of the peeling process for the Brownian half-plane in a companion paper.