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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