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- W4206341281 abstract "We give a potential-theoretic characterization of measures μ0 which have the property that the Coulomb gas, defined with respect to the prior μ0, 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 at zero temperature, in the mean field regime. This is shown to be the case for the Hausdorff measure on a compact Lipschitz hypersurface, as well as Lesbesgue measure on a bounded Lipschitz domain. We also provide constructions of priors μ0, absolutely continuous with respect to Lebesgue measure on a smoothly bounded domain, such that the corresponding 2d Coulomb exhibits a zeroth-order phase transition. This is based on relations to Ullman’s criterion in the theory of orthogonal polynomials and Bernstein-Markov inequalities." @default.
- W4206341281 created "2022-01-26" @default.
- W4206341281 creator A5073101289 @default.
- W4206341281 date "2021-01-01" @default.
- W4206341281 modified "2023-09-26" @default.
- W4206341281 title "Priors leading to well-behaved Coulomb and Riesz gases versus zeroth-order phase transitions – a potential-theoretic characterization" @default.
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- W4206341281 doi "https://doi.org/10.1214/21-ejp700" @default.
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