Priors leading to well-behaved Coulomb and Riesz gases versus zeroth-order phase transitions - a potential-theoretic characterization
Artikel i vetenskaplig tidskrift, 2021

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.

Författare

Robert Berman

Chalmers, Matematiska vetenskaper, Algebra och geometri

Göteborgs universitet

Electronic Journal of Probability

10836489 (eISSN)

Vol. 26 145 1-49

Ämneskategorier

Sannolikhetsteori och statistik

Diskret matematik

DOI

10.1214/21-EJP700

Mer information

Senast uppdaterat

2023-10-23