Superconcentration and Related Topics

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.