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: Subhroshekhar Ghosh, University of California, Berkeley
Title:   What does a Point Process Outside a Domain tell us about
         What's Inside?
Date:    Monday, January 16
Time:    14:30
Place:   Schreiber 309
In a Poisson point process we have independence between disjoint
spatial domains, so the points outside a disk give us no information
on the points inside. The story gets a lot more interesting for
processes with stronger spatial correlation. In the case of Ginibre
ensemble, a process arising from eigenvalues of random matrices, we
prove that the outside points determine exactly the number of points
inside, and further, we demonstrate that they determine nothing more.
In the case of zero ensembles of Gaussian power series, we prove that
the outside points determine exactly the number and the centre of
mass of the inside points, and nothing further. These phenomena
suggest a certain hierarchy of point processes according to their
rigidity; Poisson, Ginibre and the Gaussian power series fit in at
levels 0, 1 and 2 in this ladder. Time permitting, we will also look
at some interesting consequences of our results, with applications to
continuum percolation, reconstruction of Gaussian entire functions,
and others. This is based on joint work with Fedor Nazarov, Yuval
Peres and Mikhail Sodin.
Best regards,
Seminar webpage:
Technion Math Net-2 (TECHMATH2)
Editor: Michael Cwikel   <> 
Announcement from: Ron Peled   <>