2020/06/19 by Jean‐François Le Gall, Gall, Jean-François Le
Mathematics · #60D05 #FOS: Mathematics #Mathematical Dynamics and Fractals #Point processes and geometric inequalities #Probability (math.PR) #Stochastic processes and statistical mechanics
paper · pdf · doi:10.48550/arxiv.2006.11050
openalex publication_date 2020/06/19 · openalex created_date 2024/04/10 · openalex updated_date 2026/07/28
We provide a new construction of Brownian disks in terms of forests of continuous random trees equipped with nonnegative labels corresponding to distances from a distinguished point uniformly distributed on the boundary of the disk. This construction shows in particular that distances from the distinguished point evolve along the boundary as a five-dimensional Bessel bridge. As an important ingredient of our proofs, we show that the uniform measure on the boundary, as defined in the earlier work of Bettinelli and Miermont, is the limit of the suitably normalized volume measure on a small tubular neighborhood of the boundary. Our construction also yields a simple proof of the equivalence between the two definitions of the Brownian half-plane.