in a class of parabolic SPDEs
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2010
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54
pages
English
Documents
2010
Obtenez un accès à la bibliothèque pour le consulter en ligne En savoir plus
Niveau: Supérieur
Metastability in a class of parabolic SPDEs Nils Berglund MAPMO, Universite d'Orleans CNRS, UMR 6628 et Federation Denis Poisson Collaborators: Florent Barret, Ecole Polytechnique, Palaiseau Bastien Fernandez, CPT, CNRS, Marseille Barbara Gentz, University of Bielefeld Grenoble, 2 decembre 2010
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Metastability in a class of parabolic SPDEs Nils Berglund MAPMO, Universite d'Orleans CNRS, UMR 6628 et Federation Denis Poisson Collaborators: Florent Barret, Ecole Polytechnique, Palaiseau Bastien Fernandez, CPT, CNRS, Marseille Barbara Gentz, University of Bielefeld Grenoble, 2 decembre 2010
- configuration space
- transition path
- free energy
- stochastic lattice
- order parameter
- µ?
- supersaturated gas
- gibbs measure
Metastability
in a class of parabolic SPDEs
Nils Berglund MAPMO,Universit´ed’Orl´eans CNRS,UMR6628etFe´d´erationDenisPoisson www.univ-orleans.fr/mapmo/membres/berglund
Collaborators: Florent Barret, Ecole Polytechnique, Palaiseau Bastien Fernandez, CPT, CNRS, Marseille Barbara Gentz, University of Bielefeld
Grenoble,2d´ecembre2010
Metastability in
Examples:
•
•
•
Supercooled
physics
liquid
Supersaturated gas
Wrongly
magnetised
ferromagnet
1
Metastability in physics
Examples:
•Supercooled liquid •Supersaturated gas •Wrongly magnetised ferromagnet
.Near first-order phase transition .Nucleation implies crossing energy
barrier
1-a
Metastability in stochastic lattice models
.aLttice:Λ⊂⊂
Zd .Configuration space:X=SΛ,Sfinite set (e.g.{−1,1}) .an:HlimainotH:X →R or lattice gas)(e.g. Ising .Gibbs measure:µβ(x) = e−βH(x)/Zβ . chain with invariant measureDynamics: Markovµβ (e.g. Metropolis: Glauber or Kawasaki)
2
Metastability in stochastic lattice models
.Lattice:Λ⊂⊂Zd .Configuration space:X=SΛ,Sfinite set (e.g.{−1,1}) .imaH:nainotlH:X →R or lattice gas)(e.g. Ising .Gibbs measure:µβ(x) = e−βH(x)/Zβ .Dynamics: Markov chain with invariant measureµβ (e.g. Metropolis: Glauber or Kawasaki)
Results (forβ1) on •Transition time between + and− or empty and full configuration •Transition path •Shape of critical droplet
.Frank den Hollander,Metastability under stochastic dynamics, Stochastic Process. Appl.114(2004), 1–26. .s,reivierianEnzoOl´llaaiaVMdraaiuELarge deviations and metastability, Cambridge University Press, Cambridge, 2005.
2-a
