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Entropy Bounds and Isoperimetry
S. G. Bobkov, Syktyvkar State University, Russia, and B. Zegarlinski, Imperial College, London, England
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Memoirs of the American Mathematical Society
2005; 69 pp; softcover
Volume: 176
ISBN-10: 0-8218-3858-X
ISBN-13: 978-0-8218-3858-7
List Price: US$59
Individual Members: US$35.40
Institutional Members: US$47.20
Order Code: MEMO/176/829
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Table of Contents

  • Introduction and notations
  • Poincaré-type inequalities
  • Entropy and Orlicz spaces
  • \(\mathbf{LS}_q\) and Hardy-type inequalities on the line
  • Probability measures satisfying \(\mathbf{LS}_q\)-inequalities on the real line
  • Exponential integrability and perturbation of measures
  • \(\mathbf{LS}_q\)-inequalities for Gibbs measures with super Gaussian tails
  • \(\mathbf{LS}_q\)-inequalities and Markov semigroups
  • Isoperimetry
  • The localization argument
  • Infinitesimal version
  • Proof of Theorem 9.2
  • Euclidean distance (proof of Theorem 9.1)
  • Uniformly convex bodies
  • From isoperimetry to \(\mathbf{LS}_q\)-inequalities
  • Isoperimetric functional inequalities
  • Bibliography
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