Repulsion in low temperature $\beta$-ensembles

Abstract

We prove a result on separation of particles in a two-dimensional Coulomb plasma, which holds provided that the inverse temperature $\beta$ satisfies $\beta >1$. For large $\beta$, separation is obtained at the same scale as the conjectural Abrikosov lattice optimal separation.

A previous union bound mistake on p 8 was corrected. As a consequence, the main results are somewhat modified

References in corpus (2)

• Emergent Conformal Symmetry of Quantum Hall States on Singular surfaces
• Symmetry breaking in Laughlin's state on a cylinder

Cited by in corpus (4)

• Coulomb and Riesz gases: The known and the unknown
• The high temperature crossover for general 2D Coulomb gases
• A localization theorem for the planar Coulomb gas in an external field
• Local incompressibility estimates for the Laughlin phase