Multi-ended Markovian triangulations and robust convergence to the UIPT - ENS de Lyon - École normale supérieure de Lyon Accéder directement au contenu
Pré-Publication, Document De Travail Année : 2021

Multi-ended Markovian triangulations and robust convergence to the UIPT

Résumé

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.
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Dates et versions

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

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Citer

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

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