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

R. Dakovic, M. Denker, M. Gordin

Research output: Contribution to journalArticle

Abstract

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.

Original languageEnglish (US)
Pages (from-to)714-730
Number of pages17
JournalJournal of Mathematical Sciences (United States)
Volume219
Issue number5
DOIs
StatePublished - Dec 1 2016

All Science Journal Classification (ASJC) codes

  • Statistics and Probability
  • Mathematics(all)
  • Applied Mathematics

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