Department of Mathematics

Indian Institute of Science

Bangalore 560 012

 

SEMINAR

 

Speaker

:

 Prof. Subhroshekhar Ghosh 
Affiliation : University of California, Berkeley.

Subject Area

:

Mathematics

 

Venue

:

Lecture Hall I, Department of Mathematic

 

Time

:

3.45 p.m.- 4.45 p.m.

 

Date  

:

July13, 2011 (Wednesday)

Title

:

What does a point process outside a domain tell us about what's inside?
Abstract

:

In a Poisson point process we have independence between disjoint spatial domains, so the locations of 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 a Gaussian power series, we prove that the outside points determine exactly the number and the center of mass of the inside points, and nothing further. These phenomena suggest a certain hierarchy of point processes, where a higher order process is rigid with respect to a greater variety perturbations. Poisson, Ginibre and the Gaussian power series fit in at levels 0, 1 and 2 in this hierarchy.