تقرير
$q$-Pearson pair and moments in $q$-deformed ensembles
| العنوان: | $q$-Pearson pair and moments in $q$-deformed ensembles |
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| المؤلفون: | Forrester, Peter J, Li, Shi-Hao, Shen, Bo-Jian, Yu, Guo-Fu |
| سنة النشر: | 2021 |
| المجموعة: | Mathematics Mathematical Physics |
| مصطلحات موضوعية: | Mathematical Physics |
| الوصف: | The generalisation of continuous orthogonal polynomial ensembles from random matrix theory to the $q$-lattice setting is considered. We take up the task of initiating a systematic study of the corresponding moments of the density from two complementary viewpoints. The first requires knowledge of the ensemble average with respect to a general Schur polynomial, from which the spectral moments follow as a corollary. In the case of little $q$-Laguerre weight, a particular ${}_3 \phi_2$ basic hypergeometric polynomial is used to express density moments. The second approach is to study the $q$-Laplace transform of the un-normalised measure. Using integrability properties associated with the $q$-Pearson equation for the $q$-classical weights, a fourth order $q$-difference equation is obtained, generalising a result of Ledoux in the continuous classical cases. Comment: 31 pages. Comments are welcome |
| نوع الوثيقة: | Working Paper |
| URL الوصول: | http://arxiv.org/abs/2110.13420 |
| رقم الأكسشن: | edsarx.2110.13420 |
| قاعدة البيانات: | arXiv |
| الوصف غير متاح. |