3 papers
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.PR2025
Vanishing uniqueness thresholds in Voronoi percolation on products
Matteo D'Achille, Jan Grebík, 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…
math.PR2024
Ideal Poisson--Voronoi tessellations beyond hyperbolic spaces
Matteo D'Achille
We construct and study the ideal Poisson--Voronoi tessellation of the product of two hyperbolic planes endowed with the norm. We prove…