Physique statistique des surfaces aléatoires et combinatoire bijective des cartes planaires

Abstract : Maps are combinatorial objects arising in physics as the natural discretization of random surfaces used in two-dimensional quantum gravity or string theory, as well as in matrix models. After recalling these relations, we establish correspondences between various classes of maps and trees, that are other combinatorial objects with a simple structure. A first mathematical outcome of these constructions are bijective, elementary and rigorous proofs of several results in map enumeration. Moreover, we access to some fine information on the intrinsic geometry of maps, leading to analytical exact results thanks to an unexpected integrability property. Finally we address the question of the existence of a universal continuum limit.
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Submitted on : Monday, October 17, 2005 - 12:01:00 AM
Last modification on : Thursday, February 7, 2019 - 1:32:17 AM
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Jérémie Bouttier. Physique statistique des surfaces aléatoires et combinatoire bijective des cartes planaires. Physique mathématique [math-ph]. Université Pierre et Marie Curie - Paris VI, 2005. Français. ⟨tel-00010651⟩

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