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- W3123836634 abstract "We study Coulomb gases in any dimension $mathsf{d}geq2$ and in a broad temperature regime. We prove local laws on the energy, separation and number of points down to the microscopic scale. These yield the existence of limiting point processes after extraction, generalizing the Ginibre point process for arbitrary temperature and dimension. The local laws come together with a quantitative expansion of the free energy with a new explicit error rate in the case of a uniform background density. These estimates have explicit temperature dependence, allowing to treat regimes of very large or very small temperature, and exhibit a new minimal lengthscale for rigidity and screening, depending on the temperature. They apply as well to energy minimizers (formally zero temperature). The method is based on a bootstrap on scales and reveals the additivity of the energy modulo surface terms, via the introduction of subadditive and superadditive approximate energies." @default.
- W3123836634 created "2021-02-01" @default.
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- W3123836634 date "2021-01-01" @default.
- W3123836634 modified "2023-10-17" @default.
- W3123836634 title "Local laws and rigidity for Coulomb gases at any temperature" @default.
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- W3123836634 doi "https://doi.org/10.1214/20-aop1445" @default.
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