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Circular unitary ensembles: parametric models and their asymptotic maximum likelihood estimates. (English) Zbl 1356.81231

J. Math. Sci., New York 219, No. 5, 714-730 (2016) and Zap. Nauchn. Semin. POMI 441, 163-186 (2015).
Summary: 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, behaves as 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.

MSC:

81V35 Nuclear physics
81V17 Gravitational interaction in quantum theory
83C45 Quantization of the gravitational field
60B20 Random matrices (probabilistic aspects)

Software:

circular; CircStats
PDFBibTeX XMLCite
Full Text: DOI

References:

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