Arcsine Law as the Classical Limit for interacting Fock spaces

2013/05/13 by Hayato Saigo, Saigo, Hayato
Computer Science · Mathematics · Physics and Astronomy · #42C05 #46L53 #81S99 #Advanced Mathematical Identities #Bayesian Methods and Mixture Models #FOS: Mathematics #FOS: Physical sciences #Mathematical Physics (math-ph) #Probability (math.PR) #Random Matrices and Applications #math-ph #math.MP #math.PR #msc:42C05 #msc:46L53 #msc:81S99

paper · pdf · doi:10.48550/arxiv.1305.2666

7 pages

arxiv created 2013/05/13 · openalex publication_date 2013/05/13 · arxiv updated 2013/05/14 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

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.

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