Percolation in hyperbolic space: the non-uniqueness phase.

Resumen:

We consider Bernoulli percolation on Cayley graphs of reflection groups in the 3-dimensional hyperbolic space H^3 corresponding to a large class of Coxeter polyhedra. In such setting, we prove the existence of a non-empty no-uniqueness percolation phase, i.e., that p_c<p_u. It means that for some values of the percolation parameter there are a.s. infinitely many infinite components in the percolation subgraph.
If time permits, I will present a sketch for the case of a right angled compact polyhedron with at least 18 faces.

Posted on Apr 28, 2016 in Núcleo Modelos Estocásticos de Sistemas Complejos y Desordenados, Seminars