### Abstract

We study the classical two-dimensional one-component plasma of N positively charged point particles, interacting via the Coulomb potential and confined by an external potential. For the specific inverse temperature β= 1 (in our normalization), the charges are the eigenvalues of random normal matrices, and the model is exactly solvable as a determinantal point process. For any positive temperature, using a multiscale scheme of iterated mean-field bounds, we prove that the equilibrium measure provides the local particle density down to the optimal scale of N^{o} ^{(} ^{1} ^{)} particles. Using this result and the loop equation, we further prove that the particle configurations are rigid, in the sense that the fluctuations of smooth linear statistics on any scale are N^{o} ^{(} ^{1} ^{)}.

Original language | English (US) |
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Pages (from-to) | 189-230 |

Number of pages | 42 |

Journal | Communications In Mathematical Physics |

Volume | 356 |

Issue number | 1 |

DOIs | |

State | Published - Nov 1 2017 |

### ASJC Scopus subject areas

- Statistical and Nonlinear Physics
- Mathematical Physics

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## Cite this

*Communications In Mathematical Physics*,

*356*(1), 189-230. https://doi.org/10.1007/s00220-017-2932-8