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
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,
Seminar webpage:
Technion Math Net-2 (TECHMATH2)
Editor: Michael Cwikel   <> 
Announcement from: Ron Peled   <>