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Asymptotics of unitary and orthogonal matrix integrals |
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| Authors: | Benoît Collins Alice Guionnet |
| Institution: | a CNRS, ICJ, Lyon 1 Claude Bernard University, 43 bd du 11 Novembre 1918, 69622 Villeurbanne, France b Dept. Math. Stat., University of Ottawa, Canada c UMPA, CNRS UMR 5669, ENS Lyon, 46 allée d'Italie, 69007 Lyon, France d LPMA, Universités Paris VI, 175 rue du Chevaleret, 75013 Paris, France |
| Abstract: | In this paper, we prove that in small parameter regions, arbitrary unitary matrix integrals converge in the large N limit and match their formal expansion. Secondly we give a combinatorial model for our matrix integral asymptotics and investigate examples related to free probability and the HCIZ integral. Our convergence result also leads us to new results of smoothness of microstates. We finally generalize our approach to integrals over the orthogonal group. |
| Keywords: | 15A52 46L54 |
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