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The fundamental question of characterizing continuity and boundedness of Gaussian processes goes back to Kolmogorov. After contributions by R. Dudley and X. Fernique, it was solved by the author. This book provides an overview of "generic chaining", a completely natural variation on the ideas of Kolmogorov. It takes the reader from the first principles to the edge of current knowledge and to the open problems that remain in this domain.

The Generic Chaining: Upper and Lower Bounds for Stochastic Processes

Overview and Basic Facts.- Gaussian Processes and Related Structures.- Matching Theorems.- The Bernoulli Conjecture.- Families of distances.- Applications to Banach Space Theory.