Group representations and applied probability

Abstract

This account is meant to serve as an introduction to certain mathematical ideas which can be of considerable importance in applied probability and in statistical theory. Since a wide field is to be covered in a short space, the account has to depend on heuristic arguments and a sympathetic understanding from those familiar with the technical details of the subject is called for. Constant reference to the sources of the underlying mathematics isnotcalled for, as it will be clear that the author is not claiming these results as his own. The references at the end of the paper, which are arranged so as to aid those readers who wish to proceed further, will also indicate the sources of the mathematical and statistical ideas used. We assume some knowledge of the groups, though most concepts are defined below. By beginning from the finite dimensional case and motivating later concepts in terms of this we hope to make the later, rather technical sections, more accessible.