6 papers
Haagerup property and group-invariant percolation
Chiranjib Mukherjee, Konstantin Recke
Let be the Cayley graph of a finitely generated, infinite group . We show that has the Haagerup property if and only if for every , there is a -inva…
Coarse embeddability, -compression and Percolations on General Graphs
Chiranjib Mukherjee, Konstantin Recke
We show that a locally finite, connected graph has a coarse embedding into a Hilbert space if and only if there exist bond percolations with arbitrarily large marginals and two-poi…
Critical Poisson hyperplane percolation in hyperbolic space has no unbounded cells
Tillmann Bühler, Anna Gusakova, Konstantin Recke
We show that tessellations of hyperbolic space by isometry-invariant Poisson processes of -dimensional hyperplanes do not have an unbounded cell at the critical intensity. T…
Vanishing uniqueness thresholds in Voronoi percolation on products
Matteo D'Achille, Jan GrebÃk, 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…
Poisson-Voronoi percolation in higher rank
Jan GrebÃk, Konstantin Recke
We show that the uniqueness thresholds for Poisson-Voronoi percolation in symmetric spaces of connected higher rank semisimple Lie groups with property (T) converge to zero in the…
Schur Multipliers of -algebras, group-invariant compactification and applications to amenability and percolation
Chiranjib Mukherjee, Konstantin Recke
Let be a countable discrete group. Given any sequence of -normalized functions (), consider the associated positive definite matrix coeff…