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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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10.1007/bf02940191

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1432-2064

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Modified logarithmic Sobolev inequalities and tran

Authors: Ivan Gentil Arnaud Guillin Laurent Miclo
Publish Date: 2005/03/15
Volume: 133, Issue: 3, Pages: 409-436
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Abstract

We present a class of modified logarithmic Sobolev inequality interpolating between Poincaré and logarithmic Sobolev inequalities suitable for measures of the type exp −x α or exp −x α log β 2+x α ∈12 and β ∈ ℝ which lead to new concentration inequalities These modified inequalities share common properties with usual logarithmic Sobolev inequalities as tensorisation or perturbation and imply as well Poincaré inequality We also study the link between these new modified logarithmic Sobolev inequalities and transportation inequalities

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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. 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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