Large deviation principle for moment map estimation

Botero, Alonso and Christandl, Matthias and Vrana, Péter (2021) Large deviation principle for moment map estimation. Electronic Journal of Probability, 26 (none). ISSN 1083-6489

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Abstract

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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