Displaying similar documents to “Poisson perturbations”

Invariance of Poisson measures under random transformations

Nicolas Privault (2012)

Annales de l'I.H.P. Probabilités et statistiques

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We prove that Poisson measures are invariant under (random) intensity preserving transformations whose finite difference gradient satisfies a cyclic vanishing condition. The proof relies on moment identities of independent interest for adapted and anticipating Poisson stochastic integrals, and is inspired by the method of Üstünel and Zakai ( (1995) 409–429) on the Wiener space, although the corresponding algebra is more complex than in the Wiener case. The examples of...

Localization for Schrödinger operators with Poisson random potential

Abel Klein, Peter Hislop, François Germinet (2007)

Journal of the European Mathematical Society

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We prove exponential and dynamical localization for the Schr¨odinger operator with a nonnegative Poisson random potential at the bottom of the spectrum in any dimension. We also conclude that the eigenvalues in that spectral region of localization have finite multiplicity. We prove similar localization results in a prescribed energy interval at the bottom of the spectrum provided the density of the Poisson process is large enough.