Stieltjes Transforms and <i>R</i>-Transforms Associated with Two-Parameter Lambert–Tsallis Functions
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...
| Main Authors: | , |
|---|---|
| Format: | Article |
| Language: | English |
| Published: |
MDPI AG
2023-05-01
|
| Series: | Entropy |
| Subjects: | |
| Online Access: | https://www.mdpi.com/1099-4300/25/6/858 |
| _version_ | 1797594950587645952 |
|---|---|
| author | Hideto Nakashima Piotr Graczyk |
| author_facet | Hideto Nakashima Piotr Graczyk |
| author_sort | Hideto Nakashima |
| collection | DOAJ |
| description | 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 <i>R</i>-transformations. |
| first_indexed | 2024-03-11T02:30:58Z |
| format | Article |
| id | doaj.art-a3a02231d9784d308e215d42e2c3b6ee |
| institution | Directory Open Access Journal |
| issn | 1099-4300 |
| language | English |
| last_indexed | 2024-03-11T02:30:58Z |
| publishDate | 2023-05-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Entropy |
| spelling | doaj.art-a3a02231d9784d308e215d42e2c3b6ee2023-11-18T10:17:25ZengMDPI AGEntropy1099-43002023-05-0125685810.3390/e25060858Stieltjes Transforms and <i>R</i>-Transforms Associated with Two-Parameter Lambert–Tsallis FunctionsHideto Nakashima0Piotr Graczyk1The Institute of Statistical Mathematics, Midori-cho 10-3, Tachikawa, Tokyo 190-8562, JapanLaboratoire de Mathématiques LAREMA, Université d’Angers, 2 boulevard Lavoisier, CEDEX 01, 49045 Angers, FranceIn 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 <i>R</i>-transformations.https://www.mdpi.com/1099-4300/25/6/858random matriceseigenvalue distributionsStieltjes transformationsR-transformationsLambert–Tsallis functions |
| spellingShingle | Hideto Nakashima Piotr Graczyk Stieltjes Transforms and <i>R</i>-Transforms Associated with Two-Parameter Lambert–Tsallis Functions Entropy random matrices eigenvalue distributions Stieltjes transformations R-transformations Lambert–Tsallis functions |
| title | Stieltjes Transforms and <i>R</i>-Transforms Associated with Two-Parameter Lambert–Tsallis Functions |
| title_full | Stieltjes Transforms and <i>R</i>-Transforms Associated with Two-Parameter Lambert–Tsallis Functions |
| title_fullStr | Stieltjes Transforms and <i>R</i>-Transforms Associated with Two-Parameter Lambert–Tsallis Functions |
| title_full_unstemmed | Stieltjes Transforms and <i>R</i>-Transforms Associated with Two-Parameter Lambert–Tsallis Functions |
| title_short | Stieltjes Transforms and <i>R</i>-Transforms Associated with Two-Parameter Lambert–Tsallis Functions |
| title_sort | stieltjes transforms and i r i transforms associated with two parameter lambert tsallis functions |
| topic | random matrices eigenvalue distributions Stieltjes transformations R-transformations Lambert–Tsallis functions |
| url | https://www.mdpi.com/1099-4300/25/6/858 |
| work_keys_str_mv | AT hidetonakashima stieltjestransformsandiritransformsassociatedwithtwoparameterlamberttsallisfunctions AT piotrgraczyk stieltjestransformsandiritransformsassociatedwithtwoparameterlamberttsallisfunctions |