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math.PR2026
Convergence towards Ideal Poisson--Voronoi tessellations with a focus on Diestel--Leader graphs
Matteo D'Achille, Ali Khezeli
We provide necessary and sufficient conditions for convergence towards a unique IPVT on any proper pointed measured metric space. The conditions are that the volume function, when…
math.PR2026
Indistinguishability in One-or-Two-Ended Forests on Unimodular Random Graphs
Francois Baccelli, Ali Khezeli
Indistinguishability is a form of ergodicity, introduced by Lyons and Schramm for percolation clusters, that has become a fundamental notion in the theory of random infinite graphs…
math.PR2025
Vanishing uniqueness thresholds in Voronoi percolation on products
Matteo D'Achille, Jan GrebÃk, Ali Khezeli +2
We study Poisson--Voronoi percolation and its discrete analogue Bernoulli--Voronoi percolation in spaces with a non-amenable product structure. We develop a new method of proving s…