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Conference papers

Planar maps and Airy phenomena

Cyril Banderier 1 Philippe Flajolet 1 Gilles Schaeffer 2 Michele Soria 3
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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Submitted on : Tuesday, September 26, 2006 - 8:53:17 AM
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Cyril Banderier, Philippe Flajolet, Gilles Schaeffer, Michele Soria. Planar maps and Airy phenomena. International Colloquium on Automata, Languages, & Programming - ICALP'2000, Jul 2000, Genève, Switzerland. pp.388-402, ⟨10.1007/3-540-45022-X_33⟩. ⟨inria-00099359⟩



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