Article Dans Une Revue Annales de l'I.H.P. Probabilités et statistiques Année : 2025

Spatial Markov property in Brownian disks

Résumé

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.

Dates et versions

hal-05548253 , version 1 (11-03-2026)

Identifiants

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Jean-François Le Gall, Armand Riera. Spatial Markov property in Brownian disks. Annales de l'I.H.P. Probabilités et statistiques, 2025, 61 (3), ⟨10.1214/24-AIHP1470⟩. ⟨hal-05548253⟩
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