Group measure space construction, ergodicity and superrigidity for stable random fields

Abstract: In this work, it is established that the group measure space construction corresponding to a minimal representation is an invariant of a stationary symmetric $\alpha$-stable (S$\alpha$S) random field indexed by any countable group $G$. When $G=\mathbb{Z}^d$, we characterize ergodicity of stationary S$\alpha$S fields in terms of the central decomposition of this crossed product von Neumann algebra coming from any (not necessarily minimal) Rosinski representation. This shows that ergodicity is a $W^*$-rigid property (in a suitable sense) for this class of fields. All our results have analogues for stationary max-stable random fields as well.

probability

Audience: researchers in the topic

Bangalore Probability Seminar

Series comments: The link to zoom meeting can be found on the seminar's google calendar - www.isibang.ac.in/~d.yogesh/BPS.html