Large deviations for the two-dimensional Yang-Mills measure

摘要

This article presents a large deviations principle for the two-dimensional Yang-Mills measure, which is the first mathematical result relating the Yang-Millsmeasure on a compact surface and the Yang-Mills action. Most of the materialis issued from a paper~8 written in collaboration with James Norris. In thepresent survey, we have tried to give a simple presentation of the problemand its solution, in particular by emphasizing the analogy between the Yang-Mills situation and the more familiar large deviations results for the Brownianmotion or Brownian bridges.