Multi-ended Markovian triangulations and robust convergence to the UIPT - Archive ouverte HAL Access content directly
Preprints, Working Papers, ... Year :

Multi-ended Markovian triangulations and robust convergence to the UIPT

(1)
1

Abstract

We classify completely the infinite, planar triangulations satisfying a weak spatial Markov property, without assuming one-endedness nor finiteness of vertex degrees. In particular, the Uniform Infinite Planar Triangulation (UIPT) is the only such triangulation with average degree 6. As a consequence, we prove that the convergence of uniform triangulations of the sphere to the UIPT is robust, in the sense that it is preserved under various perturbations of the uniform measure. As another application, we obtain large deviation estimates for the number of occurencies of a pattern in uniform triangulations.
Fichier principal
Vignette du fichier
multi-ended.pdf (518.05 Ko) Télécharger le fichier
Origin : Files produced by the author(s)

Dates and versions

ensl-03481683 , version 1 (15-12-2021)

Identifiers

Cite

Thomas Budzinski. Multi-ended Markovian triangulations and robust convergence to the UIPT. 2021. ⟨ensl-03481683⟩
11 View
17 Download

Altmetric

Share

Gmail Facebook Twitter LinkedIn More