Linearization coefficients for orthogonal polynomials using stochastic processes

DOI10.1214/009117904000000757zbMath1092.05076arXivmath/0301094OpenAlexW3106202711MaRDI QIDQ2497210

Michael Anshelevich

Publication date: 3 August 2006

Published in: The Annals of Probability (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/math/0301094

zbMATH Keywords

free probabilitystochastic measurescontinuous big \(q\)-Hermite polynomials

Mathematics Subject Classification ID

Related Items (10)

Multiple Stratonovich integral and Hu-Meyer formula for Lévy processes ⋮ Fock space associated with quadrabasic Hermite orthogonal polynomials ⋮ Rényi entropies, \(L_q\) norms and linearization of powers of hypergeometric orthogonal polynomials by means of multivariate special functions ⋮ Linearization and Krein-like functionals of hypergeometric orthogonal polynomials ⋮ Semicircular limits on the free Poisson chaos: counterexamples to a transfer principle ⋮ The combinatorics of Al-Salam-Chihara \(q\)-Laguerre polynomials ⋮ Markov processes with free-Meixner laws ⋮ Conditional moments of \(q\)-Meixner processes ⋮ On linearization coefficients of \(q\)-Laguerre polynomials ⋮ On linearization coefficients of \(q\)-Laguerre polynomials

Cites Work

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• Processes with free increments
• Free stochastic measures via noncrossing partitions
• Free stochastic measures via noncrossing partitions. II.
• Aq-deformed Poisson distribution based on orthogonal polynomials
• q-Lévy processes
• Linéarisation de Produits de Polynômes de Meixner, Krawtchouk, et Charlier
• A combinatorial formula for the linearization coefficients of general Sheffer polynomials
• Partition-dependent stochastic measures and \(q\)-deformed cumulants

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