Technion, IEM faculty - Seminar in Probability and Stochastic Processes
 
Speaker: Subhro Ghosh, UC Berkeley,
 
Title: What does a point process outside a domain tell us about what is inside?
 
Date: 17/01/2012
 
Time: 11:30
 
Place: Hashmal-861
 
Abstract:  <http://ie.technion.ac.il/seminar_files/1325493828_text.txt>
 
Or read it here:
 
 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.
 
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Technion Math. Net (TECHMATH)
Editor: Michael Cwikel   <techm@math.technion.ac.il> 
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