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Circular Unitary Ensembles: Parametric Models and Their Asymptotic Maximum Likelihood Estimates

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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.

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Authors and Affiliations

  1. Georg-August-Universität, Göttingen, Germany

    R. Dakovic

  2. Pennsylvania State University, Philadelphia, USA

    M. Denker

  3. St.Petersburg Department of the Steklov Mathematical Institute, St.Petersburg, Russia

    M. Gordin

Authors
  1. R. Dakovic
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  2. M. Denker
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  3. M. Gordin
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Correspondence to M. Denker.

Additional information

M. Gordin is deceased.

Published in Zapiski Nauchnykh Seminarov POMI, Vol. 441, 2015, pp. 163–186.

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Dakovic, R., Denker, M. & Gordin, M. Circular Unitary Ensembles: Parametric Models and Their Asymptotic Maximum Likelihood Estimates. J Math Sci 219, 714–730 (2016). https://doi.org/10.1007/s10958-016-3141-2

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