$q$-Racah probability distribution
Fuente:
arXiv
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| Autori principali: | , , |
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| Natura: | Preprint |
| Pubblicazione: |
2023
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| _version_ | 1866909904002875392 |
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| author | Hayashi, Masahito Hora, Akihito Yanagida, Shintarou |
| author_facet | Hayashi, Masahito Hora, Akihito Yanagida, Shintarou |
| contents | We introduce a certain discrete probability distribution $P_{n,m,k,l;q}$ having non-negative integer parameters $n,m,k,l$ and quantum parameter $q$ which arises from a zonal spherical function of the Grassmannian over the finite field $\mathbb{F}_q$ with a distinguished spherical vector. Using representation theoretic arguments and hypergeometric summation technique, we derive the presentation of the probability mass function by a single $q$-Racah polynomial, and also the presentation of the cumulative distribution function in terms of a terminating ${}_4 ϕ_3$-hypergeometric series. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2311_09992 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | $q$-Racah probability distribution Hayashi, Masahito Hora, Akihito Yanagida, Shintarou Representation Theory Mathematical Physics Classical Analysis and ODEs Quantum Algebra We introduce a certain discrete probability distribution $P_{n,m,k,l;q}$ having non-negative integer parameters $n,m,k,l$ and quantum parameter $q$ which arises from a zonal spherical function of the Grassmannian over the finite field $\mathbb{F}_q$ with a distinguished spherical vector. Using representation theoretic arguments and hypergeometric summation technique, we derive the presentation of the probability mass function by a single $q$-Racah polynomial, and also the presentation of the cumulative distribution function in terms of a terminating ${}_4 ϕ_3$-hypergeometric series. |
| title | $q$-Racah probability distribution |
| topic | Representation Theory Mathematical Physics Classical Analysis and ODEs Quantum Algebra |
| url | https://arxiv.org/abs/2311.09992 |