Oriented percolation in one-dimensional 1/r^2 models

In this seminar, I will discuss results in collaboration with D. Marchetti and V. Sidoravicius, that regard the existence of oriented percolation for the one dimensional long range bond percolation model with occupation probabilities that decay as 1/r^2 as r tends to infinity, answering a question left open by C.M. Newman and L.S. Shulman (CMP, 104, 1986).