Extremal distance and conformal radius of a CLE_4 loop - Archive ouverte HAL Accéder directement au contenu
Pré-Publication, Document De Travail Année : 2020

Extremal distance and conformal radius of a CLE_4 loop

Distance extrémale et rayon conforme d'une boucle de CLE_4

Résumé

Consider CLE_4 in the unit disk and let $\ell$ be the loop of the CLE_4 surrounding the origin. Schramm, Sheffield and Wilson determined the law of the conformal radius seen from the origin of the domain surrounded by $\ell$. We complement their result by determining the law of the extremal distance between $\ell$ and the boundary of the unit disk. More surprisingly, we also compute the joint law of these conformal radius and extremal distance. This law involves first and last hitting times of a one-dimensional Brownian motion. Similar techniques also allow us to determine joint laws of some extremal distances in a critical Brownian loop-soup cluster.
Fichier principal
Vignette du fichier
Conformal distance.pdf (999.24 Ko) Télécharger le fichier
Origine Fichiers produits par l'(les) auteur(s)

Dates et versions

hal-02557456 , version 1 (28-04-2020)
hal-02557456 , version 2 (10-06-2020)

Identifiants

  • HAL Id : hal-02557456 , version 1

Citer

Juhan Aru, Titus Lupu, Avelio Sepúlveda. Extremal distance and conformal radius of a CLE_4 loop. 2020. ⟨hal-02557456v1⟩
90 Consultations
99 Téléchargements

Partager

Gmail Mastodon Facebook X LinkedIn More