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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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10.1002/clc.20314

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1432-2064

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Zerotemperature Glauber dynamics on mathbbZ

Authors: Robert Morris
Publish Date: 2009/12/11
Volume: 149, Issue: 3-4, Pages: 417-434
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Abstract

We study zerotemperature Glauber dynamics on mathbbZd which is a dynamic version of the Ising model of ferromagnetism Spins are initially chosen according to a Bernoulli distribution with density p and then the states are continuously and randomly updated according to the majority rule This corresponds to the sudden quenching of a ferromagnetic system at high temperature with an external field to one at zero temperature with no external field Define p cmathbbZd to be the infimum over p such that the system fixates at ‘ + ’ with probability 1 It is a folklore conjecture that p cmathbbZd = 1/2 for every 2 le d in mathbbN We prove that p cmathbbZd to 1/2 as d → ∞

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Other Papers In This Journal:
  1. Loss without recovery of Gibbsianness during diffusion of continuous spins
  2. On the Dirichlet problem for asymmetric zero-range process on increasing domains
  3. Propagation and conditional propagation of chaos for pressureless gas equations
  4. Wasserstein space over the Wiener space
  5. Markov processes on partitions
  6. Quasi-stationary distributions for structured birth and death processes with mutations
  7. Outliers in the spectrum of iid matrices with bounded rank perturbations
  8. Product of random projections, Jacobi ensembles and universality problems arising from free probability
  9. Poincaré type inequalities on the discrete cube and in the CAR algebra
  10. The largest eigenvalue of small rank perturbations of Hermitian random matrices
  11. Invariance principle for the random conductance model
  12. Modified logarithmic Sobolev inequalities and transportation inequalities
  13. Asymptotic statistical equivalence for scalar ergodic diffusions
  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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