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.

UR - http://www.scopus.com/inward/record.url?scp=84994296469&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=84994296469&partnerID=8YFLogxK

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 -