Quantum and classical random walks

Abstract: 

Quantum as well as classical random walks give a nice playground for the use of harmonic analysis, the theory of special functions, combinatorics, group representation theory, functional analysis, complex analysis, ...to deal with problems of applied interest arising in physics, mathematical biology, financial math, network theory, computer science, etc.

I will try to give an ab-initio description of both subjects and try to put emphasis on their similarites and differences. The classical case is indeed very classical with papers going at least back to 1770, while the quantum case started developing around 1993 under the impetus of quantum computing.