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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
Table of Contents
Chapters
- 1. Introduction and notations
- 2. Poincaré-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