Large deviation principle for moment map estimation

被引：2
作者：
Botero, Alonso [1 ]
Christandl, Matthias [2 ]
Vrana, Peter [3 ,4 ]
机构：
[1] Univ Los Andes, Dept Fis, Cra 1 18A-12, Bogota, Colombia
[2] Univ Copenhagen, Dept Math Sci, QMATH, Univ Pk 5, DK-2100 Copenhagen, Denmark
[3] Budapest Univ Technol & Econ, MTA BME Lendulet Quantum Informat Theory Res Grp, Egry Jozsef U 1, H-1111 Budapest, Hungary
[4] Budapest Univ Technol & Econ, Inst Math, Egry Jozsef U 1, H-1111 Budapest, Hungary
来源：
ELECTRONIC JOURNAL OF PROBABILITY | 2021年 / 26卷
基金：
欧洲研究理事会;
关键词：
large deviation principle; compact Lie group; moment map; quantum measurement; RANDOM-WALK; PRODUCT; MULTIPLICITIES; SYSTEMS;
D O I：
10.1214/21-EJP636
中图分类号：
O21 [概率论与数理统计]; C8 [统计学];
学科分类号：
020208 ; 070103 ; 0714 ;
摘要：
Given a representation of a compact Lie group and a state we define a probability measure on the coadjoint orbits of the dominant weights by considering the decomposition into irreducible components. For large tensor powers and independent copies of the state we show that the induced probability distributions converge to the value of the moment map. For faithful states we prove that the measures satisfy the large deviation principle with an explicitly given rate function.
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页数：23
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