# Planar maps and Airy phenomena

2 POLKA - Polynomials, Combinatorics, Arithmetic
INRIA Lorraine, LORIA - Laboratoire Lorrain de Recherche en Informatique et ses Applications
3 CALFOR - Calcul formel
LIP6 - Laboratoire d'Informatique de Paris 6
Abstract : A considerable number of asymptotic distributions arising in random combinatorics and analysis of algorithms are of the exponential-quadratic type $(e^{-x^2})$, that is, Gaussian. We exhibit here a new class of universal'' phenomena that are of the exponential-cubic type ($e^{ix^3}$), corresponding to nonstandard distributions that involve the Airy function. Such Airy phenomena are expected to be found in a number of applications, when confluences of critical points and singularities occur. About a dozen classes of planar maps are treated in this way, leading to the occurrence of a common Airy distribution that describes the sizes of cores and of largest (multi)connected components. Consequences include the analysis and fine optimization of random generation algorithms for multiply connected planar graphs.
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Type de document :
Communication dans un congrès
U. Montanari, J. Rolim, E. Welzl. International Colloquium on Automata, Languages, & Programming - ICALP'2000, Jul 2000, Genève, Switzerland. Springer, 1853, pp.388-402, 2000, Lecture Notes in Computer Science. 〈10.1007/3-540-45022-X_33〉
Domaine :

https://hal.inria.fr/inria-00099359
Contributeur : Publications Loria <>
Soumis le : mardi 26 septembre 2006 - 08:53:17
Dernière modification le : jeudi 22 novembre 2018 - 14:45:33

### Citation

Cyril Banderier, Philippe Flajolet, Gilles Schaeffer, Michele Soria. Planar maps and Airy phenomena. U. Montanari, J. Rolim, E. Welzl. International Colloquium on Automata, Languages, & Programming - ICALP'2000, Jul 2000, Genève, Switzerland. Springer, 1853, pp.388-402, 2000, Lecture Notes in Computer Science. 〈10.1007/3-540-45022-X_33〉. 〈inria-00099359〉

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