Quantum Probability and Spectral Analysis of Graphs

Abstract

In the rest of this book we shall discuss asymptotic analysis for adjacency matrices and representations of the symmetric groups from the viewpoint of quantum probability theory. The purpose of this chapter is to assemble basic notions and tools in representation theory of the symmetric groups. Most materials are standard though the analytic description of Young diagrams, which is essential for the study of asymptotic behaviour of a representation of S(n) as n would be less familiar to the readers. This fantastic idea is due to Vershik and Kerov.