# Priors leading to well-behaved Coulomb and Riesz gases versus zeroth-order phase transitions – a potential-theoretic characterization

@article{Berman2018PriorsLT,
title={Priors leading to well-behaved Coulomb and Riesz gases versus zeroth-order phase transitions – a potential-theoretic characterization},
author={Robert J Berman},
journal={Electronic Journal of Probability},
year={2018}
}
• R. Berman
• Published 26 November 2018
• Mathematics
• Electronic Journal of Probability
We give a potential-theoretic characterization of measures µ 0 which have the property that the Coulomb gas, deﬁned with respect to the prior µ 0 , is “well-behaved” and similarly for more general Riesz gases. This means that the laws of the empirical measures of the corresponding random point process satisfy a Large Deviation Principle with a rate functional which depends continuously on the temperature, in the sense of Gamma-convergence. Equivalently, there is no zeroth-order phase transition…
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