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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Detalles Bibliográficos
Clasificación:Libro Electrónico
Autor principal: Chatterjee, Sourav (Autor)
Autor Corporativo: SpringerLink (Online service)
Formato: Electrónico eBook
Idioma:Inglés
Publicado: Cham : Springer International Publishing : Imprint: Springer, 2014.
Edición:1st ed. 2014.
Colección:Springer Monographs in Mathematics,
Temas:
Probabilities.
Mathematical physics.
System theory.
Probability Theory.
Mathematical Physics.
Complex Systems.
Theoretical, Mathematical and Computational Physics.
Acceso en línea:Texto Completo
Tabla de Contenidos:
  • 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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