TEL AVIV UNIVERSITY - HOROWITZ SEMINAR Dear all, This week at the Horowitz seminar on Probability, Ergodic Theory and Dynamical Systems at Tel Aviv University we are happy to have: Speaker: Johan Tykesson, Weizmann Institute Title: Percolation in the vacant set of Poisson cylinders Date: Monday, April 4 Time: 14:30 Place: Schreiber 210 NOTE SPECIAL ROOM!!! Abstract: We consider a Poisson point process on the space of lines in R^d, where a multiplicative factor u>0 of the intensity measure determines the density of lines. Each line in the process is taken as the axis of a bi-infinite cylinder of radius 1. We investigate percolative properties of the vacant set, defined as the subset of R^d that is not covered by any such cylinder. We show that in dimensions d >= 4, there is a critical value u_*(d) \in (0,\infty), such that with probability 1, the vacant set has an unbounded component if u<u_*(d), and only bounded components if u>u_*(d). For d=3, we prove that the vacant set does not percolate for large u and that the vacant set intersected with a two-dimensional subspace of R^d does not even percolate for small u>0. This is joint work with David Windisch. Best regards, Ron Seminar webpage: <http://www.math.tau.ac.il/~peledron/Horowitz_seminar/Horowitz_seminar.html> --------------------------------------------------------- Technion Math Net-2 (TECHMATH2) Editor: Michael Cwikel <techm@math.technion.ac.il> Announcement from: Ron Peled <peledron@gmail.com>