Department of Mathematics
Indian Institute of Science
Bangalore 560 012
SEMINAR
Speaker |
: |
Dr. Parthanil Roy |
Affiliation | : |
ETH Zurich and Michigan State University |
Subject Area |
: |
Mathematics
|
Venue |
: |
Lecture Hall - I, Dept of Mathematics
|
Time |
: |
2.00 pm
|
Date |
: |
December 7,2007 (Friday) |
Title |
: |
Ergodic theory, abelian groups, and point processes associated with stable random fields |
Abstract | : |
We consider a point process sequence induced by a stationary symmetric -stable (0 < < 2) discrete parameter random eld. It is easy to prove, following the arguments in the one-dimensional case in Resnick and Samorodnitsky (2004), that if the random eld is generated by a dissipative group action then the point process sequence converges weakly to a cluster Poisson process. For the conservative case, no general result is known even in the one-dimensional case. We look at a specic class of stable random elds generated by conservative actions whose eective dimensions can be computed using the structure theorem of nitely generated abelian groups. The corresponding point processes sequence is not tight and hence needs to be properly normalized in order to ensure weak convergence. This weak limit is computed using extreme value theory and some counting techniques. (This talk is based on a joint work with Gennady Samorodnitsky). |