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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 Berlin Heidelberg

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DOI

10.1002/14651858.CD001900

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1432-2064

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A simple proof of exponential decay of subcritical

Authors: Jan M Swart
Publish Date: 2016/09/13
Volume: 170, Issue: 1-2, Pages: 1-9
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Abstract

This paper gives a new simple proof of the known fact that for contact processes on general lattices in the subcritical regime the expected number of infected sites decays exponentially fast as time tends to infinity The proof also yields an explicit bound on the survival probability below the critical recovery rate which shows that the critical exponent associated with this function is bounded from below by its meanfield value The main idea of the proof is that if the expected number of infected sites decays slower than exponentially then this implies the existence of a harmonic function that can be used to show that the process survives for any lower value of the recovery rate

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  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
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  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. Zero-temperature Glauber dynamics on $${\mathbb{Z}^d}$$
  15. Selector processes on classes of sets
  16. The divergence of Banach space valued random variables on Wiener space
  17. Large deviations for many Brownian bridges with symmetrised initial-terminal condition
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