Large Deviations for the Yang-Mills Measure on a Compact Surface |
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| Authors: | Thierry Lévy James R. Norris |
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| Affiliation: | (1) CNRS, Département de Mathématiques et Applications, école Normale Supérieure, 45, rue d'Ulm, 75005 Paris, France;(2) Statistical Laboratory, Centre for Mathematical Sciences, Wilberforce Road, Cambridge, CB3 0WB, UK |
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| Abstract: | 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 scaled 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. |
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