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math.PR2018
One-point boundaries of ends of clusters in percolation in
Jan Czajkowski
Consider Bernoulli bond percolation on a graph nicely embedded in hyperbolic space in such a way that it admits a transitive action by isometries of . Le…
math.PR2015
Percolation in the hyperbolic space: non-uniqueness phase and fibrous clusters
Jan Czajkowski
In this thesis, I am going to consider Bernoulli percolation on graphs admitting vertex-transitive actions of groups of isometries of d-dimensional hyperbolic spaces H^d. In the fi…
math.PR2013★ 1 cited
Non-uniqueness phase of Bernoulli percolation on reflection groups for some polyhedra in H^3
Jan Czajkowski
In the present paper I consider Cayley graphs of reflection groups of finite-sided Coxeter polyhedra in 3-dimensional hyperbolic space H^3, with standard sets of generators. As the…