Superconcentration and Related Topics

Inbunden, Engelska, 2014

Av Sourav Chatterjee

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Based on the author's lectures at Cornell Probability Summer School in 2012, this book links the concept of superconcentration with probability theory. Includes a number of open problems for professional mathematicians and exercises for graduate students.

Produktinformation

Utgivningsdatum2014-01-22
Mått155 x 235 x 17 mm
Vikt410 g
FormatInbunden
SpråkEngelska
SerieSpringer Monographs in Mathematics
Antal sidor156
Upplaga2014
FörlagSpringer International Publishing AG
ISBN9783319038858

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Sourav Chatterjee is a Professor of Statistics and Mathematics at Stanford University. He has previously taught at the University of California at Berkeley and at the Courant Institute of Mathematical Sciences. He has won several international awards for his work in probability theory, including the Rollo Davidson Prize (2010), the Doeblin Prize (2012) and the Loève Prize (2013) and has received the invitation to speak at the International Congress of Mathematicians in 2014.

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.