Superconcentration and Related Topics

• Κύριος συγγραφέας: Chatterjee, Sourav (Συγγραφέας)
• Συγγραφή απο Οργανισμό/Αρχή: SpringerLink (Online service)
• Μορφή: Ηλεκτρονική πηγή Ηλ. βιβλίο
• Γλώσσα: English
• Έκδοση: Cham : Springer International Publishing : Imprint: Springer, 2014.
• Σειρά: Springer Monographs in Mathematics,
• Θέματα: Mathematics.; Probabilities.; Mathematical physics.; Statistical physics.; Dynamical systems.; Probability Theory and Stochastic Processes.; Mathematical Physics.; Statistical Physics, Dynamical Systems and Complexity.

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 of areas of probability theory...

Πίνακας περιεχομένων:

• 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.