Nonsingular Gaussian actions: Beyond the mixing case

Weak Mixing Properties for Nonsingular Actions

For a general group G we consider various weak mixing properties of nonsingular actions. In the case where the action is actually measure preserving all these properties coincide, and our purpose here is to check which implications persist in the nonsingular case.

Nonsingular Group Actions

This paper deals with measurable stationary symmetric stable random fields indexed by R and their relationship with the ergodic theory of nonsingular R-actions. Based on the phenomenal work of Rosiński (2000), we establish extensions of some structure results of stationary SαS processes to SαS fields. Depending on the ergodic theoretical nature of the underlying action, we observe different beh...

Rank One Power Weakly Mixing Nonsingular Transformations

We show that Chacon's nonsingular type III transformation T , 0 < 1, is power weakly mixing, i.e., for all sequences of nonzero integers fk1; : : : ; krg, T k1 : : : T kr is ergodic. We then show that in in nite measure, this condition is not implied by in nite ergodic index (having all nite Cartesian products ergodic), and that in nite ergodic index does not imply 2-recurrence.

Maharam Extension for Nonsingular Group Actions

Property (T) and the Furstenberg Entropy of Nonsingular Actions

We establish a new characterization of property (T) in terms of the Furstenberg entropy of nonsingular actions. Given any generating measure μ on a countable group G, A. Nevo showed that a necessary condition for G to have property (T) is that the Furstenberg μ-entropy values of the ergodic, properly nonsingular G-actions are bounded away from zero. We show that this is also a sufficient condit...