Nakashima Hideto, Graczyk Piotr
The Institute of Statistical Mathematics, Midori-cho 10-3, Tachikawa, Tokyo 190-8562, Japan.
Laboratoire de Mathématiques LAREMA, Université d'Angers, 2 boulevard Lavoisier, CEDEX 01, 49045 Angers, France.
Entropy (Basel). 2023 May 27;25(6):858. doi: 10.3390/e25060858.
In this paper, we study a two-parameter family of Stieltjes transformations related to holomorphic Lambert-Tsallis functions, which are a two-parameter generalization of the Lambert function. Such Stieltjes transformations appear in the study of eigenvalue distributions of random matrices associated with some growing statistically sparse models. A necessary and sufficient condition on the parameters is given for the corresponding functions being Stieltjes transformations of probabilistic measures. We also give an explicit formula of the corresponding -transformations.
在本文中，我们研究了一族与全纯兰伯特 - 塔利斯函数相关的双参数斯蒂尔杰斯变换，兰伯特 - 塔利斯函数是兰伯特函数的双参数推广。此类斯蒂尔杰斯变换出现在与一些增长的统计稀疏模型相关的随机矩阵特征值分布的研究中。给出了参数的一个充要条件，使得相应函数为概率测度的斯蒂尔杰斯变换。我们还给出了相应(\mathcal{L}) - 变换的显式公式。
