研究課題/領域番号 |
16K17616
|
研究機関 | 九州大学 |
研究代表者 |
Trinh Khanh・Duy 九州大学, マス・フォア・インダストリ研究所, 助教授 (00726127)
|
研究期間 (年度) |
2016-04-01 – 2019-03-31
|
キーワード | random Jacobi matrices / Gaussian beta ensembles / Wishart beta ensembles / Jacobi beta ensembles / spectral measures / localization |
研究実績の概要 |
The purpose of this research is to exploit new spectral properties of Gaussian beta ensembles, in particular, and of random Jacobi matrices, in general. Let me mention two main achievements last year. (i) I propose a universal approach to study the limiting behavior of the spectral measures of random Jacobi matrices. As an application to Gaussian beta ensembles, the convergence and Gaussian fluctuation around the semicircle distribution are derived. It can be also applicable to Wishart and Jacobi beta ensembles. (ii) Consider Gaussian beta ensembles in the regime that the parameter beta tends to zero with additional constraint, we show the Gaussian fluctuations for eigenvalues and Poisson statistics for the bulk statistics. This is a joint work with Professor Fumihiko Nakano (Gakushuin University).
|
現在までの達成度 (区分) |
現在までの達成度 (区分)
2: おおむね順調に進展している
理由
A general approach to study spectral measures of random Jacobi matrices was proposed and some connection with classical theory of Random Jacobi matrices was established. Two papers were written, one has been accepted to be published.
|
今後の研究の推進方策 |
The next plan is to study the limiting behavior of Gaussian beta ensembles in a double scaling regime and related random Jacobi matrices. We are interested in both the global (linear statistics) and local (bulk statistics) limiting behaviors.
|
次年度使用額が生じた理由 |
The plan of buying some books is changed into next years.
|
次年度使用額の使用計画 |
To buy some books related to probability theory.
|