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 β is 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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Yattselev, M.L. Large deviations and linear statistics for potential theoretic ensembles associated with regular closed sets. Probab. Theory Relat. Fields 156, 827–850 (2013). https://doi.org/10.1007/s00440-012-0444-1
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DOI: https://doi.org/10.1007/s00440-012-0444-1
Keywords
- Normal matrix model
- Potential theoretic ensembles
- Large deviation principle
- Linear statistics
Mathematics Subject Classification (2000)
- 60F10
- 15B52
- 15A18
- 31A15