Circular Unitary Ensembles: Parametric Models and Their Asymptotic Maximum Likelihood Estimates
- 作者: Dakovic R.1, Denker M.2, Gordin M.3
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隶属关系:
- Georg-August-Universität
- Pennsylvania State University
- St.Petersburg Department of the Steklov Mathematical Institute
- 期: 卷 219, 编号 5 (2016)
- 页面: 714-730
- 栏目: Article
- URL: https://journals.rcsi.science/1072-3374/article/view/238661
- DOI: https://doi.org/10.1007/s10958-016-3141-2
- ID: 238661
如何引用文章
详细
Parametrized families of distributions for the circular unitary ensemble in random matrix theory are considered; they are connected to Toeplitz determinants and have many applications in mathematics (for example, to the longest increasing subsequences of random permutations) and physics (for example, to nuclear physics and quantum gravity). We develop a theory for the unknown parameter estimated by an asymptotic maximum likelihood estimator, which, in the limit, behavesas the maximum likelihood estimator if the latter is well defined and the family is sufficiently smooth. They are asymptotically unbiased and normally distributed, where the norming constants are unconventional because of long range dependence.
作者简介
R. Dakovic
Georg-August-Universität
Email: mhd13@psu.edu
德国, Göttingen
M. Denker
Pennsylvania State University
编辑信件的主要联系方式.
Email: mhd13@psu.edu
美国, Philadelphia
M. Gordin
St.Petersburg Department of the Steklov Mathematical Institute
Email: mhd13@psu.edu
俄罗斯联邦, St.Petersburg