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math.PR2018
The sharp phase transition for level set percolation of smooth planar Gaussian fields
Stephen Muirhead, Hugo Vanneuville
We prove that the connectivity of the level sets of a wide class of smooth centred planar Gaussian fields exhibits a phase transition at the zero level that is analogous to the pha…
math.PR2018
Annealed scaling relations for Voronoi percolation
Hugo Vanneuville
We prove annealed scaling relations for planar Voronoi percolation. To our knowledge, this is the first result of this kind for a continuum percolation model. We are mostly inspire…
math.PR2018
Quantitative quenched Voronoi percolation and applications
Hugo Vanneuville
Ahlberg, Griffiths, Morris and Tassion have proved that, asymptotically almost surely, the quenched crossing probabilities for critical planar Voronoi percolation do not depend on…