Abstract
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 \(\mathbb {C}\) with weakly admissible external fields \(Q\) and very general measures \(\nu \) on \(K\). For this we use logarithmic potential theory in \(\mathbb {R}^{n}\), \(n\ge 2\), and a standard contraction principle in large deviation theory which we apply from the two-dimensional sphere in \(\mathbb {R}^{3}\) to the complex plane \(\mathbb {C}\).
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Communicated by Doron Lubinsky.
This paper is dedicated to our good friend and colleague, Ed Saff.
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Bloom, T., Levenberg, N. & Wielonsky, F. Logarithmic Potential Theory and Large Deviation. Comput. Methods Funct. Theory 15, 555–594 (2015). https://doi.org/10.1007/s40315-015-0120-4
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DOI: https://doi.org/10.1007/s40315-015-0120-4