Partition Scheme for Families of Distances

Abstract

In Chapter 10 we turn to other processes such that the description of the tails of their increments requires an entire sequence of parameters, and therefore a whole sequence of distances on the index space. As an application we consider the situation of “canonical processes”, where the r.v.s X _t are linear combinations of independent copies of symmetric r.v.s with density proportional to exp(−|x|^α) where α≥1 (and to considerably more general situations as discovered by R. Latała). The size of the process can then be completely described as a function of the geometry of the index space, a far reaching extension of the Gaussian case.