Abstract
We use tridiagonal models to study the limiting behavior of β-Laguerre and β-Jacobi ensembles, focusing on the limiting behavior of the extremal eigenvalues and the central limit theorem for the two ensembles. For the central limit theorem of β-Laguerre ensembles, we follow the idea in [1] while giving a modified version for the generalized case. Then we use the total variation distance between the two sorts of ensembles to obtain the limiting behavior of β-Jacobi ensembles.
Original language | English |
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Pages (from-to) | 2025-2039 |
Number of pages | 15 |
Journal | Acta Mathematica Scientia |
Volume | 42 |
Issue number | 5 |
DOIs | |
Publication status | Published - 2022 |
Bibliographical note
Green Open Access added to TU Delft Institutional Repository 'You share, we take care!' - Taverne project https://www.openaccess.nl/en/you-share-we-take-careOtherwise as indicated in the copyright section: the publisher is the copyright holder of this work and the author uses the Dutch legislation to make this work public.
Keywords
- 15B52
- 60B20
- 60F10
- beta-ensembles
- central limit theorem
- largest and smallest eigenvalues
- total variation distance