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In this talk we will give a new proof for a question that was first
posed by Jonasson, Mossel and Peres, concerning percolation on a
randomly stretched planar lattice. More specifically, we fix a parameter
q in (0, 1) and we slash the lattice Z^2 in the following way. For every
vertical line that crosses the x axis along an integer value, we toss an
independent coin and with probability q we remove all edges along that
line. Then we do the same with the horizontal lines that cross the y
axis at integer values. We are then left with a graph G that looks like
a randomly stretched version of Z^2 and on top of which we would like to
perform i.i.d. Bernoulli percolation. The question at hand is whether
this percolation features an non-trivial phase transition, or more
precisely, whether p_c(G) < 1. Although this question has been
previously solved in a seminal article by Hoffman, we present here an
alternative solution that greatly simplifies the exposition. We also
explain how the presented techniques can be used to prove the existence
of a phase transition for other models with minimal changes to the proof.

This talk is based on a joint work with M. Hilário, M. Sá and R. Sanchis.

https://ucdavis.zoom.us/j/99375733459