Complementarity and Stochastic Independence

A mathematical approach to the notion of complementarity in quantum physics is described and its historical development is shortly reviewed. After that, the notion of n-complementarity is introduced as a natural extension of complementarity and at the same time as weak form of stochastic independence. Several examples in which n-complementarity is realized but not independence are produced. The construction of these examples is based on the structure of Interacting Fock Space (IFS) that is strictly related to the classical theory of orthogonal polynomials. A brief description of both this notion and this connection is included to make the paper self-contained.