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