4 papers
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…
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…
Products of Infinite Countable Groups Have Fixed Price One
Ali Khezeli
We prove that the product of any two infinite countable groups has fixed price one. This resolves a longstanding problem posed by Gaboriau. The proof uses the propagation method to…
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…