Tel Aviv University 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: Tom Meyerovitch, Ben-Gurion University Title: On equivariant thinning, allocation and matching schemes for Poisson processes Date: Monday, January 7 Time: 14:30 Place: Schreiber 309 Abstract: Poisson thinning, allocation and matching are ``natural'' operations on a realization of a Poisson process which have been considered in the literature. A Poisson thinning, for instance, is a rule for selecting a subset of the points in the Poisson process which are equal in distribution to a lower intensity Poisson process. There are interesting and non-trivial constructions of isometry-equivariant Poisson thinning, Poisson allocation and Poisson matching. In this talk I will consider the existence of operations of the above types which are equivariant with respect to a group of measure-preserving transformations other than isometries. Evans proved that the only linear transformations which admit equivariant Poisson thinning are isometries. I will show that no equivariant thinning, allocation or matching is possible with respect to any conservative and ergodic measure preserving transformation. My proof is based on an ergodicity result which uses Kean's classic ``ergodic multiplier theorem''. The definitions involved will be given during the talk, no background with Poisson processes is assumed. 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@post.tau.ac.il>