Onsdagen den 15 maj klockan 14.00 (OBS! Tiden) håller Johan Tykesson, Uppsala universitet, ett seminarium med titeln The Poisson cylinder model in Euclidean space.
Sammanfattning: 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. First, 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). We then move on to study the geometry of the union of all the cylinders in the process. It turns out that this union is always a connected set. Morever, any two points $x$ and $y$ that are contained in the union of the cylinders, are connected via a sequence of at most $d$ cylinders.
The talk is based on joint works with David Windisch and Erik Broman.
Lokalen är Cramérrummet, rum 306, hus 6 i Kräftriket.