  Interacting Fock space connects the study of quantum probability theory,
classical random variables, and orthogonal polynomials. It is a pre-Hilbert
space associated with creation, preservation, and annihilation processes. We
prove that if three processes are asymptotically commutative, the arcsine law
arises as the "large quantum number limits." As a corollary, it is shown that
for many probability measures, asymptotic behavior of orthogonal polynomials is
described by the arcsine function. A weaker form of asymptotic commutativity
provides us a discretized arcsine law.
