Repulsion in low temperature $\beta$-ensembles
Probability
2017-12-06 v3 Mathematical Physics
Complex Variables
math.MP
Abstract
We prove a result on separation of particles in a two-dimensional Coulomb plasma, which holds provided that the inverse temperature satisfies . For large , separation is obtained at the same scale as the conjectural Abrikosov lattice optimal separation.
Cite
@article{arxiv.1701.04796,
title = {Repulsion in low temperature $\beta$-ensembles},
author = {Yacin Ameur},
journal= {arXiv preprint arXiv:1701.04796},
year = {2017}
}
Comments
A previous union bound mistake on p 8 was corrected. As a consequence, the main results are somewhat modified