Dualité de Schur-Weyl, mouvement brownien sur les groupes de Lie compacts classiques et étude asymptotique de la mesure de Yang-Mills

Abstract : In the following text, we are interested in the study of Lie-groups valued random variables. We give a deformation of the Weingarten calculus introduced by Benoît Collins and Piotr Sniady. We study the asymptotic behavior of Brownian motion on compact Lie groups in high dimensions and obtain new fluctuations results. Two new objects called the planar gaussian master field and the planar oriented master field are introduced here to describe the asymptotic behavior of the Yang-Mills measure as the dimension of the structure group is large.
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Antoine Dahlqvist. Dualité de Schur-Weyl, mouvement brownien sur les groupes de Lie compacts classiques et étude asymptotique de la mesure de Yang-Mills. Mathématiques générales [math.GM]. Université Pierre et Marie Curie - Paris VI, 2014. Français. ⟨NNT : 2014PA066012⟩. ⟨tel-00961035v3⟩

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