Arcsine Law as the Classical Limit for interacting Fock spaces

TL;DR

This paper explores how interacting Fock spaces can generalize quantum-classical correspondence, demonstrating that the Arcsine Law emerges as a classical limit for certain symmetric probability measures like q-Gaussians.

Contribution

It introduces a framework linking algebraic probability and orthogonal polynomials, showing the Arcsine Law as a classical limit in this context.

Findings

Arcsine Law as classical limit for symmetric measures

Extension to q-Gaussians and other probability measures

Discussion of asymmetric measures like exponential distribution

Abstract

In the present paper we discuss how to generalize ``Quantum-Classical Correspondence'' by means of the notion of interacting Fock spaces, which associates algebraic probability theory and the theory of orthogonal polynomials of probability measures. As an application we show that the Arcsine Law is ``Classical Limit'' for interacting Fock spaces corresponnding to certain kind of symmetric probability measures such as q-Gaussians. We also discuss the case of the exponential distribution as a simple example of asymmetric probability measures.