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Conference Papers Year : 2000

Planar maps and Airy phenomena


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.

Dates and versions

inria-00099359 , version 1 (26-09-2006)



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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