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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.GR2025
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…