## Abstract

This paper studies the large deviations of the empirical measure associated with n independent random variables with a degenerate limiting distribution as n?8. A large deviations principle - quite unlike the classical Sanov type results - is established for such empirical measures in a general Polish space setting. This result is applied to the large deviations for the empirical process of a system of interacting particles, in which the diffusion coefficient vanishes as the number of particles tends to infinity. A second way in which the present example differs from previous work on similar weakly interacting systems is that there is a singularity in the mean-field type interaction. © 1993 Springer-Verlag.

Original language | English |
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Pages (from-to) | 179-193 |

Number of pages | 15 |

Journal | Probability Theory and Related Fields |

Volume | 97 |

Issue number | 1-2 |

DOIs | |

Publication status | Published - Mar 1993 |

## Keywords

- Mathematics Subject Classification (1991): 60F10