Large deviations for the Yang-Mills measure on a compact surface

Thierry Lévy (1) , James Norris (2)

1 DMA - Département de Mathématiques et Applications - ENS Paris
2 Statistical Laboratory [Cambridge]

We prove the first mathematical result relating the Yang-Mills measure on a compact surface and the Yang-Mills energy. We show that, at the small volume limit, the Yang-Mills measures satisfy a large deviation principle with a rate function which is expressed in a simple and natural way in terms of the Yang-Mills energy.

Mots clés: Large deviation principle; Yang-Mills measure; Sobolev connections

Domaines: Physique mathématique [math-ph]; Géométrie différentielle [math.DG]; Probabilités [math.PR]

Thierry Lévy, James Norris. Large deviations for the Yang-Mills measure on a compact surface. 2005. ⟨hal-00002089v3⟩