Vector energy and large deviation

For d nonpolar compact sets K 1 , …, K d ⊂ ℂ, admissible weights Q 1 , …, Q d and a positive semidefinite interaction matrix C = ( c i, j ) i, j =1, …, d with no zero column, we define natural discretizations of the weighted energy of a d -tuple of positive measures µ = (µ 1 , …, µ d ) ∈ M r ( K ),...

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Bibliographic Details
Published in:Journal d'analyse mathématique (Jerusalem) 2015, Vol.125 (1), p.139-174
Main Authors: Bloom, T., Levenberg, N., Wielonsky, F.
Format: Article
Language:English
Subjects:
Abstract Harmonic Analysis
Analysis
Deviation
Discretization
Dynamical Systems and Ergodic Theory
Functional Analysis
Mathematical analysis
Mathematics
Mathematics and Statistics
Partial Differential Equations
Texts
Vectors (mathematics)
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Summary:For d nonpolar compact sets K 1 , …, K d ⊂ ℂ, admissible weights Q 1 , …, Q d and a positive semidefinite interaction matrix C = ( c i, j ) i, j =1, …, d with no zero column, we define natural discretizations of the weighted energy of a d -tuple of positive measures µ = (µ 1 , …, µ d ) ∈ M r ( K ), where µ j is supported in K j and has mass r j . We have an L ∞ -type discretization W (µ) and an L 2 -type discretization J (µ) defined using a fixed measure ν = ( ν 1 , …, ν d ). This leads to a large deviation principle for a canonical sequence { σ k } of probability measures on M r ( K ) if ν is a strong Bernstein-Markov measure.
ISSN:0021-7670
1565-8538
DOI:10.1007/s11854-015-0005-5