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Optimal local laws and CLT for the circular Riesz gas

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arxiv 2112.05881 v5 pith:GK7TBIHW submitted 2021-12-11 math.PR math-phmath.MP

Jeanne Boursier This is my paper
classification math.PRmath-phmath.MP
keywords localrieszfunctionslawsmethodanalysisargumentscentral
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We study the long-range one-dimensional Riesz gas on the circle, a continuous system of particles interacting through a Riesz kernel. We establish near-optimal rigidity estimates on gaps valid at any scale. Leveraging these local laws together with Stein's method, we prove a quantitative Central Limit Theorem for linear statistics. The proof is based on a mean-field transport and a fine analysis of the fluctuations of local error terms using various convexity and monotonicity arguments. Using a comparison principle for the Helffer-Sj\"ostrand equation, the method can handle very singular test functions, including characteristic functions of intervals.

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Cited by 2 Pith papers

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