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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.CO2025
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…