Article Dans Une Revue The Annals of Probability Année : 2022

Isoperimetric inequalities in the Brownian plane

Résumé

We consider the model of the Brownian plane, which is a pointed noncompact random metric space with the topology of the complex plane. The Brownian plane can be obtained as the scaling limit in distribution of the uniform infinite planar triangulation or the uniform infinite planar quadrangulation and is conjectured to be the universal scaling limit of many others random planar lattices. We establish sharp bounds on the probability of having a short cycle separating the ball of radius r centered at the distinguished point from infinity. Then we prove a strong version of the spatial Markov property of the Brownian plane. Combining our study of short cycles with this strong spatial Markov property we obtain sharp isoperimetric bounds for the Brownian plane.

Dates et versions

hal-05546568 , version 1 (10-03-2026)

Identifiants

Citer

Armand Riera. Isoperimetric inequalities in the Brownian plane. The Annals of Probability, 2022, 50 (5), ⟨10.1214/22-aop1576⟩. ⟨hal-05546568⟩
21 Consultations
0 Téléchargements

Altmetric

Partager

  • More