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Journal Articles Annales de l'Institut Henri Poincaré (B) Probabilités et Statistiques Year : 2022

Counter examples to invariant circle packing

Abstract

In this work, a unimodular random planar triangulation is constructed that has no invariant circle packing. This disputes a problem asked in [9]. A natural weaker problem is the existence of point-stationary circle pack-ings for a graph, which are circle packings that satisfy a certain mass transport principle. It is shown that the answer to this weaker problem is also false. Two examples are provided with two different approaches: Using indistinguishability and finite approximations

Dates and versions

hal-03924954 , version 1 (05-01-2023)

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Ali Khezeli. Counter examples to invariant circle packing. Annales de l'Institut Henri Poincaré (B) Probabilités et Statistiques, 2022, 58 (4), ⟨10.1214/21-AIHP1234⟩. ⟨hal-03924954⟩
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