Linearization coefficients for orthogonal polynomials using stochastic processes
| dc.creator | Anshelevich, Michael | |
| dc.date | 2003-01-10 | |
| dc.date | 2005-04-06 | |
| dc.date.accessioned | 2026-07-07T04:54:21Z | |
| dc.date.available | 2026-07-07T04:54:21Z | |
| dc.description | Given a basis for a polynomial ring, the coefficients in the expansion of a product of some of its elements in terms of this basis are called linearization coefficients. These coefficients have combinatorial significance for many classical families of orthogonal polynomials. Starting with a stochastic process and using the stochastic measures machinery introduced by Rota and Wallstrom, we calculate and give an interpretation of linearization coefficients for a number of polynomial families. The processes involved may have independent, freely independent or q-independent increments. The use of noncommutative stochastic processes extends the range of applications significantly, allowing us to treat Hermite, Charlier, Chebyshev, free Charlier and Rogers and continuous big q-Hermite polynomials. We also show that the q-Poisson process is a Markov process. | |
| dc.description | Published at http://dx.doi.org/10.1214/009117904000000757 in the Annals of Probability (http://www.imstat.org/aop/) by the Institute of Mathematical Statistics (http://www.imstat.org) | |
| dc.identifier | https://arxiv.org/abs/math/0301094 | |
| dc.identifier | http://arxiv.org/abs/math/0301094 | |
| dc.identifier | Annals of Probability 2005, Vol. 33, No. 1, 114-136 | |
| dc.identifier | doi:10.1214/009117904000000757 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/66219 | |
| dc.subject | Combinatorics | |
| dc.subject | Classical Analysis and ODEs | |
| dc.subject | Operator Algebras | |
| dc.subject | 05E35 (Primary) 05A18, 05A30, 46L53, 60G51. (Secondary) | |
| dc.title | Linearization coefficients for orthogonal polynomials using stochastic processes | |
| dc.type | text |