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### Abstract

The two-dimensional one-component plasma is an ubiquitous model for several vortex systems. For special values of the coupling constant βq2 (where q is the particles charge and β the inverse temperature), the model also corresponds to the eigenvalues distribution of normal matrix models. Several features of the system are discussed in the limit of large number N of particles for generic values of the coupling constant. We show that the statistics of a class of radial observables produces a rich phase diagram, and their asymptotic behaviour in terms of large deviation functions is calculated explicitly, including next-to-leading terms up to order 1/N. We demonstrate a split-off phenomenon associated to atypical fluctuations of the edge density profile. We also show explicitly that a failure of the fluid phase assumption of the plasma can break a genuine 1/N-expansion of the free energy. Our findings are corroborated by numerical comparisons with exact finite-N formulae valid for βq2 = 2.

Original language | English |
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Pages (from-to) | 1062–1081 |

Number of pages | 20 |

Journal | Journal of Statistical Physics |

Volume | 164 |

Issue number | 5 |

Early online date | 7 Jul 2016 |

DOIs | |

Publication status | Published - Sep 2016 |

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## Projects

- 2 Finished

## Cite this

Cunden, F., Mezzadri, F., & Vivo, P. (2016). Large deviations of radial statistics in the two-dimensional one-component plasma.

*Journal of Statistical Physics*,*164*(5), 1062–1081. https://doi.org/10.1007/s10955-016-1577-x