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Title of Journal: Probab Theory Relat Fields

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Abbravation: Probability Theory and Related Fields

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Springer-Verlag

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10.1016/0091-2182(88)90203-0

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1432-2064

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Loss without recovery of Gibbsianness during diffu

Authors: Christof Külske Frank Redig
Publish Date: 2005/09/12
Volume: 135, Issue: 3, Pages: 428-456
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Abstract

For `high temperature initial measures we prove that the timeevoved measure μ t is Gibbsian for all t For `low temperature initial measures we prove that μ t stays Gibbsian for small enough times t but loses its Gibbsian character for large enough t In contrast to the analogous situation for discretespin Gibbs measures there is no recovery of the Gibbs property for large t in the presence of a nonvanishing external magnetic field All of our results hold for any dimension d≥2 This example suggests more generally that timeevolved continuousspin models tend to be nonGibbsian more easily than their discretespin counterparts

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  1. On the Dirichlet problem for asymmetric zero-range process on increasing domains
  2. Propagation and conditional propagation of chaos for pressureless gas equations
  3. Wasserstein space over the Wiener space
  4. Markov processes on partitions
  5. Quasi-stationary distributions for structured birth and death processes with mutations
  6. Outliers in the spectrum of iid matrices with bounded rank perturbations
  7. Product of random projections, Jacobi ensembles and universality problems arising from free probability
  8. Poincaré type inequalities on the discrete cube and in the CAR algebra
  9. The largest eigenvalue of small rank perturbations of Hermitian random matrices
  10. Invariance principle for the random conductance model
  11. Modified logarithmic Sobolev inequalities and transportation inequalities
  12. Asymptotic statistical equivalence for scalar ergodic diffusions
  13. Zero-temperature Glauber dynamics on $${\mathbb{Z}^d}$$
  14. Selector processes on classes of sets
  15. The divergence of Banach space valued random variables on Wiener space
  16. A simple proof of exponential decay of subcritical contact processes
  17. Large deviations for many Brownian bridges with symmetrised initial-terminal condition
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