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...

Full description

Saved in:
Bibliographic Details
Published in:Constructive approximation 2018-02, Vol.47 (1), p.119-140
Main Authors: Bloom, Tom, Levenberg, Norman, Wielonsky, Franck
Format: Article
Language:English
Subjects:
Analysis
Deviation
Manifolds (mathematics)
Markov processes
Mathematics
Mathematics and Statistics
Numerical Analysis
Citations: Items that this one cites
Items that cite this one
Online Access:Get full text
Tags: Add Tag
No Tags, Be the first to tag this record!
Description
Summary: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 that satisfies a mass-density condition will also satisfy this strong Bernstein–Markov property.
ISSN:0176-4276
1432-0940
DOI:10.1007/s00365-017-9396-0