Logarithmic Potential Theory and Large Deviation

We derive a general large deviation principle for a canonical sequence of probability measures, having its origins in random matrix theory, on unbounded sets K of C with weakly admissible external fields Q and very general measures ν on K . For this we use logarithmic potential theory in R n , n ≥ 2...

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Bibliographic Details
Published in:Computational methods and function theory 2015-12, Vol.15 (4), p.555-594
Main Authors: Bloom, T., Levenberg, N., Wielonsky, F.
Format: Article
Language:English
Subjects:
Analysis
Computational Mathematics and Numerical Analysis
Functions of a Complex Variable
Mathematics
Mathematics and Statistics
Probability
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Summary:We derive a general large deviation principle for a canonical sequence of probability measures, having its origins in random matrix theory, on unbounded sets K of C with weakly admissible external fields Q and very general measures ν on K . For this we use logarithmic potential theory in R n , n ≥ 2 , and a standard contraction principle in large deviation theory which we apply from the two-dimensional sphere in R 3 to the complex plane C .
ISSN:1617-9447
2195-3724
DOI:10.1007/s40315-015-0120-4