## Bernoulli

### Moderate deviations for mean-field Gibbs measures

#### Abstract

We present a moderate-deviations principle around non-degenerate attractors of the empirical measure of random variables distributed according to a mean-field Gibbs measure. We state a result for a large class of densities of the Gibbs measure. This result is an application of a rank-dependent moderate-deviations principle for a collection of $U$-empirical measures. The results are applied for diffusion processes with mean-field interaction leading to a McKean--Vlasov limit, and to the Curie--Weiss model.

#### Article information

Source
Bernoulli, Volume 9, Number 1 (2003), 67-95.

Dates
First available in Project Euclid: 6 November 2003

https://projecteuclid.org/euclid.bj/1068129011

Digital Object Identifier
doi:10.3150/bj/1068129011

Mathematical Reviews number (MathSciNet)
MR1963673

Zentralblatt MATH identifier
1029.60021

#### Citation

Eichelsbacher, Peter; Zajic, Tim. Moderate deviations for mean-field Gibbs measures. Bernoulli 9 (2003), no. 1, 67--95. doi:10.3150/bj/1068129011. https://projecteuclid.org/euclid.bj/1068129011