| 摘要: |
| 本文研究了β-Hermite系综关于β-Laguerre系综在Kullback-Leibler距离和全变差距离下逼近的问题.利用Pinsker不等式和β-Hermite系综的中心极限定理以及β-Laguerre系综的三阶矩,我们获得了两种距离下逼近的充要条件.此结果推广了文献[4]中的结果. |
| 关键词: Beta-Hermite系综 Beta-Laguerre系综 Kullback-Leibler距离 全变差距离 |
| DOI： |
| 分类号:O211.4 |
| 基金项目:国家自然科学基金资助(NSFC12171038;11871008). |
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| APPROXIMATION OF β-LAGUERRE ENSEMBLES BY β-HERMITE ENSEMBLES |
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CAI Meng-chun1, LEI Liang-zhen2, MA Yu-tao1
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1.School of Mathematical Sciences & Laboratory of Mathematics and Complex Systems of Ministry of Education, Beijing Normal University, Beijing 100875, China;2.School of Mathematical Science, Capital Normal University, Beijing 100048, China
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| Abstract: |
| In this note, we consider the approximation of beta-Laguerre ensembles by beta-Hermite ensembles with respect to the total variation distance and the Kullback-Leibler divergence. Utilizing the Pinsker inequality, the central limit theorem of beta-Hermite ensembles and the explicit expression on the third moment of beta-Laguerre ensembles, we are able to offer sufficient and necessary conditions to this approximation. This result extends that in [4]. |
| Key words: $\beta$-Laguerre ensembles $\beta$-Hermite ensembles Kullback-Leibler divergence total variation distance |
