Infinite dimensional dynamics associated to quadratic Hamiltonians

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Publié par

Niveau: Supérieur, Doctorat, Bac+8
Innite dimensional dynamics associated to quadratic Hamiltonians Olivier Garet Institut Élie Cartan Nancy Campus Scientique BP 239 F-54506 Vandoeuvre-lès-Nancy Cedex E-Mail: Abstract We study here RZd-valued gradient diusions associated to quadratic inter- actions. We establish that each each Gaussian Gibbs measure associated to this interaction can be obtained as limit in time of the solution of the linear diusion for a set of initial deterministic conditions which we describe. Thus the absence of phase transition corresponds to the ergodicity of the system. Moreover, we study the inuence of a phase transition on the speed of con- vergence. Finally, we prove that the invariant measures for these gradient diusions are exactly the associated Gibbs measures. AMS Classications : 28D05, 60H10, 60K35, 82B26, 82C31. KEY-WORDS : Gibbsian eld, Gaussian eld, phase transition, ergodicity, innite-dimensional diusion, invariant measure. 1

  • called partition function

  • gaussian

  • diusion equation

  • ?n ?

  • innite-dimensional diusion

  • linear diusion

  • gradient dynamics

  • measure associated

  • gibbs measure

  • gradient


Publié le : mercredi 20 juin 2012
Lecture(s) : 46
Source : iecn.u-nancy.fr
Nombre de pages : 33
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