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In the present paper we discuss how to generalize ``Quantum-ClassicalCorrespondence'' by means of the notion of interacting Fock spaces, whichassociates algebraic probability theory and the theory of orthogonalpolynomials of probability measures. As an application we show that the ArcsineLaw is ``Classical Limit'' for interacting Fock spaces corresponnding tocertain kind of symmetric probability measures such as q-Gaussians. We alsodiscuss the case of the exponential distribution as a simple example ofasymmetric probability measures.

Arcsine Law as the Classical Limit for interacting Fock spaces