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Multi-ended Markovian triangulations and robust convergence to the UIPT

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.
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Preprints, Working Papers, ...
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Contributor : Thomas Budzinski Connect in order to contact the contributor
Submitted on : Wednesday, December 15, 2021 - 2:32:19 PM
Last modification on : Tuesday, January 4, 2022 - 6:11:40 AM


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  • HAL Id : ensl-03481683, version 1
  • ARXIV : 2110.15185



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



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