TY - JOUR
T1 - Circular Unitary Ensembles
T2 - Parametric Models and Their Asymptotic Maximum Likelihood Estimates
AU - Dakovic, R.
AU - Denker, M.
AU - Gordin, M.
N1 - Publisher Copyright:
© 2016, Springer Science+Business Media New York.
PY - 2016/12/1
Y1 - 2016/12/1
N2 - 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.
AB - 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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U2 - 10.1007/s10958-016-3141-2
DO - 10.1007/s10958-016-3141-2
M3 - Article
AN - SCOPUS:84994296469
SN - 1072-3374
VL - 219
SP - 714
EP - 730
JO - Journal of Mathematical Sciences (United States)
JF - Journal of Mathematical Sciences (United States)
IS - 5
ER -