Introduction

Abstract

Consider a large collection of random variables (H _s)_s≤M. What is the value of the largest of them? More generally, what is the structure of the “few largest” values? Certainly the question is too general. Even if the variables are identically distributed, the answer depends upon both the distribution and the correlation structure of the variables. When the variables are independent, then of course, everything can be computed. To inove beyond that case, one should ask what correlation structures arc of interest. A collection of random variables is, in other words, a stochastic process. The examples that first come to mind arc indexed by the real line. The correlation structure one will consider will naturally take advantage of the structure of the real line, a “one-dimensional” object.