Diffusions with Gaussian Drifts

  • Tomasz Komorowski
  • Claudio Landim
  • Stefano Olla
Part of the Grundlehren der mathematischen Wissenschaften book series (GL, volume 345)

Abstract

We continue our investigation of the passive tracer model introduced in Chap.  11 under an additional assumption that the drift is Gaussian. In this case the generator of the environment process satisfies the graded sector condition introduced in Sect.  2.7.4. Using this approach we reprove first the central limit theorem for diffusions whose drift has a finite Péclet number. This result can be extended to some classes of time dependent flows whose Péclet number are infinite by taking into account time decorrelation properties of the drift. We apply the variational principles derived in Chap.  4 to prove that the sufficient conditions for the central limit theorem obtained in this way are in some sense optimal. We give examples of families of isotropic flows for which the motion of a tracer is superdiffusive.

Keywords

Variational Principle Central Limit Theorem Stochastic Differential Equation Spectral Measure Environment Process 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© Springer-Verlag Berlin Heidelberg 2012

Authors and Affiliations

  • Tomasz Komorowski
    • 1
    • 2
  • Claudio Landim
    • 3
    • 4
  • Stefano Olla
    • 5
  1. 1.Institute of MathematicsMaria Curie-Skłodowska UniversityLublinPoland
  2. 2.Institute of MathematicsPolish Academy of SciencesWarsawPoland
  3. 3.Instituto de Matemática (IMPA)Rio de JaneiroBrazil
  4. 4.CNRS UMR 6085Université de RouenSaint-Étienne-du-RouvrayFrance
  5. 5.CEREMADE, CNRS UMR 7534Université Paris-DauphineParisFrance

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