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math.PR2019
Counter Examples to Invariant Circle Packing
Ali Khezeli
In this work, a unimodular random planar triangulation is constructed that has no invariant circle packing. This disputes a problem asked in [arXiv:1910.01614]. A natural weaker pr…
math.PR2018
Unimodular Billingsley and Frostman Lemmas
François Baccelli, Mir-Omid Haji-Mirsadeghi, Ali Khezeli
The notions of unimodular Minkowski and Hausdorff dimensions are defined in [arXiv:1807.02980] for unimodular random discrete metric spaces. The present paper is focused on the con…
math.PR2018
Unimodular Hausdorff and Minkowski Dimensions
François Baccelli, Mir-Omid Haji-Mirsadeghi, Ali Khezeli
This work introduces two new notions of dimension, namely the unimodular Minkowski and Hausdorff dimensions, which are inspired from the classical analogous notions. These dimensio…