A large deviation principle for weighted Riesz interactions

We prove a large deviation principle for the sequence of push-forwards of empirical measures in the setting of Riesz potential interactions on compact subsets $K$ in $R^d$ with continuous external fields. Our results are valid for base measures on $K$ satisfying a strong Bernstein-Markov type property for Riesz potentials. Furthermore, we give sufficient conditions on K (which are satisfied if $K$ is a smooth submanifold) so that a measure on $K$ which satisfies a mass-density condition will also satisfy this strong Bernstein-Markov property.


Publication Date:
Oct 23 2017
Date Submitted:
Mar 01 2019
Pagination:
119-140
Citation:
Constructive Approximation, 47, 1
Note:
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 Record created 2019-03-01, last modified 2019-04-03


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