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Ergodicity in infinite Hamiltonian systems with conservative noise
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  • Published: November 1996

Ergodicity in infinite Hamiltonian systems with conservative noise

  • Carlangelo Liverani1 &
  • Stefano Olla2 

Probability Theory and Related Fields volume 106, pages 401–445 (1996)Cite this article

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  • 6 Citations

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Summary.

We study the stationary measures of an infinite Hamiltonian system of interacting particles in ℝ 3 subject to a stochastic local perturbation conserving energy and momentum. We prove that the translation invariant measures that are stationary for the deterministic Hamiltonian dynamics, reversible for the stochastic dynamics, and with finite entropy density, are convex combination of “Gibbs” states. This result implies hydrodynamic behavior for the systems under consideration.

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Authors and Affiliations

  1. II Università di Roma “Tor Vergata”, Dipartimento di Matematica, I-00133 Roma, Italy , , , , , , IT

    Carlangelo Liverani

  2. Centre de Mathématiques Appliquées, Ecole Polytechnique, F-91128 Palaiseau Cedex, France and Politecnico di Torino, Dipartimento di Matematica, corso Duca degli Abruzzi 24, I-10129 Torino, Italy, , , , , , FR

    Stefano Olla

Authors
  1. Carlangelo Liverani
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  2. Stefano Olla
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Received: 17 December 1994/In revised form: 12 April 1996

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Liverani, C., Olla, S. Ergodicity in infinite Hamiltonian systems with conservative noise. Probab Theory Relat Fields 106, 401–445 (1996). https://doi.org/10.1007/s004400050071

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  • Issue Date: November 1996

  • DOI: https://doi.org/10.1007/s004400050071

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  • Mathematics Subject classification (1991): 82B21
  • 82C21
  • 82B03
  • 60Y60
  • 60F10
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