Superconcentration and Related Topics

A certain curious feature of random objects, introduced by the author as "super concentration," and two related topics, "chaos" and "multiple valleys," are highlighted in this book. Although super concentration has established itself as a recognized feature in a number...

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Détails bibliographiques
Cote:Libro Electrónico
Auteur principal: Chatterjee, Sourav (Auteur)
Collectivité auteur: SpringerLink (Online service)
Format: Électronique eBook
Langue:Inglés
Publié: Cham : Springer International Publishing : Imprint: Springer, 2014.
Édition:1st ed. 2014.
Collection:Springer Monographs in Mathematics,
Sujets:
Probabilities.
Mathematical physics.
System theory.
Probability Theory.
Mathematical Physics.
Complex Systems.
Theoretical, Mathematical and Computational Physics.
Accès en ligne:Texto Completo
Table des matières:
  • Preface
  • 1.Introduction
  • 2.Markov semigroups
  • 3.Super concentration and chaos
  • 4.Multiple valleys
  • 5.Talagrand's method for proving super concentration
  • 6.The spectral method for proving super concentration
  • 7.Independent flips
  • 8.Extremal fields
  • 9.Further applications of hypercontractivity
  • 10.The interpolation method for proving chaos
  • 11.Variance lower bounds
  • 12.Dimensions of level sets
  • Appendix A. Gaussian random variables
  • Appendix B. Hypercontractivity
  • Bibliography
  • Indices.

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