Classical beta ensembles and related eigenvalues processes at high temperature and the Markov--Krein transform
Fuente:
arXiv
Gespeichert in:
| Hauptverfasser: | , , |
|---|---|
| Format: | Preprint |
| Veröffentlicht: |
2024
|
| Schlagworte: | |
| Online-Zugang: | |
| Tags: |
Tag hinzufügen
Keine Tags, Fügen Sie den ersten Tag hinzu!
|
| _version_ | 1866918021546639360 |
|---|---|
| author | Nakano, Fumihiko Trinh, Hoang Dung Trinh, Khanh Duy |
| author_facet | Nakano, Fumihiko Trinh, Hoang Dung Trinh, Khanh Duy |
| contents | The aim of this paper is to identify the limit in a high temperature regime of classical beta ensembles on the real line and related eigenvalue processes by using the Markov--Krein transform. We show that the limiting measure of Gaussian beta ensembles (resp.\ beta Laguerre ensembles and beta Jacobi ensembles) is the inverse Markov--Krein transform of the Gaussian distribution (resp.\ the gamma distribution and the beta distribution). At the process level, we show that the limiting probability measure-valued process is the inverse Markov--Krein transform of a certain 1d stochastic process. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2412_01015 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Classical beta ensembles and related eigenvalues processes at high temperature and the Markov--Krein transform Nakano, Fumihiko Trinh, Hoang Dung Trinh, Khanh Duy Probability Mathematical Physics 60B20, 60H05 The aim of this paper is to identify the limit in a high temperature regime of classical beta ensembles on the real line and related eigenvalue processes by using the Markov--Krein transform. We show that the limiting measure of Gaussian beta ensembles (resp.\ beta Laguerre ensembles and beta Jacobi ensembles) is the inverse Markov--Krein transform of the Gaussian distribution (resp.\ the gamma distribution and the beta distribution). At the process level, we show that the limiting probability measure-valued process is the inverse Markov--Krein transform of a certain 1d stochastic process. |
| title | Classical beta ensembles and related eigenvalues processes at high temperature and the Markov--Krein transform |
| topic | Probability Mathematical Physics 60B20, 60H05 |
| url | https://arxiv.org/abs/2412.01015 |