Seminarium i matematisk statistik den 15 maj kl. 14.00
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.