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Journal of the American Mathematical Society

Published by the American Mathematical Society, the Journal of the American Mathematical Society (JAMS) is devoted to research articles of the highest quality in all areas of pure and applied mathematics.

ISSN 1088-6834 (online) ISSN 0894-0347 (print)

The 2020 MCQ for Journal of the American Mathematical Society is 4.79.

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Toward the Fourier law for a weakly interacting anharmonic crystal
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by Carlangelo Liverani and Stefano Olla PDF
J. Amer. Math. Soc. 25 (2012), 555-583 Request permission


For a system of weakly interacting anharmonic oscillators, perturbed by an energy-preserving stochastic dynamics, we prove an autonomous (stochastic) evolution for the energies at large time scale (with respect to the coupling parameter). It turns out that this macroscopic evolution is given by the so-called conservative (nongradient) Ginzburg-Landau system of stochastic differential equations. The proof exploits hypocoercivity and hypoellipticity properties of the uncoupled dynamics.
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Additional Information
  • Carlangelo Liverani
  • Affiliation: Dipartimento di Matematica, II Università di Roma (Tor Vergata), Via della Ricerca Scientifica, 00133 Roma, Italy
  • Email:
  • Stefano Olla
  • Affiliation: CEREMADE, UMR CNRS 7534, Université Paris-Dauphine, 75775 Paris-Cedex 16, France and INRIA - Université Paris Est, CERMICS, Projet MICMAC, Ecole des Ponts ParisTech, 6 & 8 Av. Pascal, 77455 Marne-la-Vallée Cedex 2, France
  • Email:
  • Received by editor(s): January 18, 2011
  • Received by editor(s) in revised form: November 6, 2011
  • Published electronically: December 1, 2011
  • Additional Notes: This paper has been partially supported by the European Advanced Grant Macroscopic Laws and Dynamical Systems (MALADY) (ERC AdG 246953), by Agence Nationale de la Recherche, under grant ANR-07-BLAN-2-184264 (LHMSHE), and by MIUR under the grant PRIN 2007B3RBEY
  • © Copyright 2011 American Mathematical Society
    The copyright for this article reverts to public domain 28 years after publication.
  • Journal: J. Amer. Math. Soc. 25 (2012), 555-583
  • MSC (2010): Primary 82C70, 60F17, 80A20
  • DOI:
  • MathSciNet review: 2869027