• Corpus ID: 249847760

Optimal local laws and CLT for the circular Riesz gas

@inproceedings{Boursier2021OptimalLL,
  title={Optimal local laws and CLT for the circular Riesz gas},
  author={Jeanne Boursier},
  year={2021}
}
We study the long-range one-dimensional Riesz gas on the circle, a continuous system of particles interacting through a Riesz (i.e inverse power) kernel. We establish near-optimal rigidity estimates on gaps valid at any scale. Leveraging on these local laws and using a Stein method, we provide a quantitative Central Limit Theorem for linear statistics. The proof is based on a mean-field transport and on a fine analysis of the fluctuations of local error terms through the study of Helffer-Sj…