Can I read Priors leading to well-behaved Coulomb and Riesz gases versus zeroth-order phase transitions -- a potential-theoretic characterization on EtoBox?

Priors leading to well-behaved Coulomb and Riesz gases versus zeroth-order phase transitions -- a potential-theoretic characterization by Berman, Robert J. is a scholarly article available to read on EtoBox.

What is Priors leading to well-behaved Coulomb and Riesz gases versus zeroth-order phase transitions -- a potential-theoretic characterization about?

We give a potential-theoretic characterization of priors which have the property that the corresponding Coulomb gas 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, 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.

Author

Berman, Robert J.

Published

2018

Language

EN