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arXiv · 1207.0718

Large Deviations and Linear Statistics for Potential Theoretic Ensembles Associated with Regular Closed Sets

Maxim L. Yattselev
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Abstract

A two-dimensional statistical model of N charged particles interacting via logarithmic repulsion in the presence of an oppositely charged regular closed region K whose charge density is determined by its equilibrium potential at an inverse temperature βis investigated. When the charge on the region, s, is greater than N, the particles accumulate in a neighborhood of the boundary of K, and form a point process in the complex plane. We describe the weak* limits of the joint intensities of this point process and show that it is exponentially likely to find the process in a neighborhood of the equilibrium measure for K.

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Maxim L. Yattselev. 2012-07-03. Large Deviations and Linear Statistics for Potential Theoretic Ensembles Associated with Regular Closed Sets. https://arxiv.org/abs/1207.0718

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