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Entropy bounds and isoperimetry

About this Title

S. G. Bobkov and B. Zegarlinski

Publication: Memoirs of the American Mathematical Society
Publication Year: 2005; Volume 176, Number 829
ISBNs: 978-0-8218-3858-7 (print); 978-1-4704-0430-7 (online)
DOI: https://doi.org/10.1090/memo/0829
MathSciNet review: 2146071
MSC: Primary 46E35; Secondary 42B35, 46E30, 46N30, 47D07, 82C20

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Table of Contents

Chapters

  • 1. Introduction and notations
  • 2. PoincarĂ©-type inequalities
  • 3. Entropy and Orlicz spaces
  • 4. $\mathrm {LS}_q$ and Hardy-type inequalities on the line
  • 5. Probability measures satisfying $\mathrm {LS}_q$-inequalities on the real line
  • 6. Exponential integrability and perturbation of measures
  • 7. $\mathrm {LS}_q$-inequalities for Gibbs measures with super Gaussian tails
  • 8. $\mathrm {LS}_q$-inequalities and Markov semigroups
  • 9. Isoperimetry
  • 10. The localization argument
  • 11. Infinitesimal version
  • 12. Proof of Theorem 9.2
  • 13. Euclidean distance (proof of Theorem 9.1)
  • 14. Uniformly convex bodies
  • 15. From isoperimetry to $\mathrm {LS}_q$-inequalities
  • 16. Isoperimetric functional inequalities