*Tid:* **18 februari 2008 kl 15.15-17.00 **
*Plats :* **Seminarierummet 3733**, Institutionen för
matematik, KTH, Lindstedts väg 25, plan 7. Karta!
*Föredragshållare:*
**
Parthanil Roy, ETH Zurich and Michigan State University
**
**Titel:**
Ergodic theory, abelian groups, and point processes associated with stable
random fields
**Sammanfattning:**
We consider a point process sequence induced by a stationary symmetric
α-stable (0 < α < 2) discrete parameter random field.
It is easy to prove,
following the arguments in the one-dimensional case in Resnick and
Samorodnitsky
(2004), that if the random field 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 specific class of stable random fields generated by conservative
actions
whose effective dimensions can be computed using the structure theorem of
finitely
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
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