# Nonsingular Poisson Suspensions

@article{Danilenko2020NonsingularPS, title={Nonsingular Poisson Suspensions}, author={Alexandre I. Danilenko and Zemer Kosloff and Emmanuel Roy}, journal={Journal d'Analyse Math{\'e}matique}, year={2020}, volume={146}, pages={741-790} }

The classical Poisson functor associates to every infinite measure preserving dynamical system ( X, μ, T ) a probability preserving dynamical system ( X *, μ*, T * ) called the Poisson suspension of T . In this paper we generalize this construction: a subgroup Aut 2 ( X, μ ) of μ -nonsingular transformations T of X is specified as the largest subgroup for which T * is μ *-nonsingular. The topological structure of this subgroup is studied. We show that a generic element in Aut 2 ( X, μ ) is…

## 6 Citations

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Abstract It is proved that each Gaussian cocycle over a mildly mixing Gaussian transformation is either a Gaussian coboundary or sharply weak mixing. The class of non-singular infinite direct…

### Generic nonsingular Poisson suspension is of type $III_1$

- Mathematics
- 2020

It is shown that for a dense $G_\delta$-subset of the subgroup of nonsingular transformations (of a standard infinite $\sigma$-finite measure space) whose Poisson suspensions are nonsingular, the…

### BERNOULLI ACTIONS OF TYPE III WITH PRESCRIBED ASSOCIATED FLOW

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- 2022

We prove that many, but not all, injective factors arise as crossed products by nonsingular Bernoulli actions of the group
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### Krieger’s type for ergodic non-singular Poisson actions of non-(T) locally compact groups

- MathematicsErgodic Theory and Dynamical Systems
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It is shown that each locally compact second countable non-(T) group G admits non-strongly ergodic weakly mixing IDPFT Poisson actions of any possible Krieger type. These actions are amenable if…

### Generic non-singular Poisson suspension is of type III1

- MathematicsErgodic Theory and Dynamical Systems
- 2021

Abstract It is shown that for a dense
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-subset of the subgroup of non-singular transformations (of a standard infinite
$\sigma $
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### Krieger’s type of nonsingular Poisson suspensions and IDPFT systems

- Mathematics
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Given an infinite countable discrete amenable group $\Gamma$, we construct explicitly sharply weak mixing nonsingular Poisson $\Gamma$-actions of each Krieger's type: $III_\lambda$, for…

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It is shown that for a dense $G_\delta$-subset of the subgroup of nonsingular transformations (of a standard infinite $\sigma$-finite measure space) whose Poisson suspensions are nonsingular, the…

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