1 citations · 1 across the 7 of their papers we have counts for
8 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…
Concentration for random Euclidean combinatorial optimization
Matteo D'Achille, Francesco Mattesini, Dario Trevisan
We prove concentration bounds for random Euclidean combinatorial optimization problems with --costs. For bipartite matching and for the (mono- and bi-partite) traveling salesper…
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…
On minimal shapes and isoperimetric constants in hyperbolic lattices
Matteo D'Achille, Vanessa Jacquier, Wioletta M. Ruszel
We fully characterize the set of finite shapes with minimal perimeter on hyperbolic lattices given by regular tilings of the hyperbolic plane whose tiles are regular -gons meeti…
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…
Local limit of massive spanning forests on the complete graph
Matteo D'Achille, Nathanaël Enriquez, Paul Melotti
We identify the local limit of massive spanning forests on the complete graph. This generalizes a well-known theorem of Grimmett on the local limit of uniform spanning trees on the…
Ideal Poisson-Voronoi tessellations on hyperbolic spaces
Matteo D'Achille, Nicolas Curien, Nathanaël Enriquez +2
We study the limit in low intensity of Poisson--Voronoi tessellations in hyperbolic spaces for . In contrast to the Euclidean setting, a limiting nontri…
Using stochastic order to compare different Euclidean Random Assignment Problems
Matteo D'Achille, Yuqi Liu
This paper provides a theorem to compare the minimum total cost of two different Euclidean Random Assignment Problems with the same number of points, using the stochastic order of…