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Planar Maps and Airy Phenomena

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Automata, Languages and Programming (ICALP 2000)

Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 1853))

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Abstract

A considerable number of asymptotic distributions arising in random combinatorics and analysis of algorithms are of the exponentialquadratic 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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Author information

Authors and Affiliations

  1. Algorithms Project, INRIA, Rocquencourt, 78150, Le Chesnay, France

    Cyril Banderier & Philippe Flajolet

  2. Loria, CNRS, Campus scientifique, B.P. 239, 54506, Vandœuvre-lés-Nancy, France

    Gilles Schaeffer

  3. Lip6, Université Paris 6, 8 rue du Capitaine Scott, 75005, Paris, France

    Michéle Soria

Authors
  1. Cyril Banderier
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  2. Philippe Flajolet
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  3. Gilles Schaeffer
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  4. Michéle Soria
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Editor information

Editors and Affiliations

  1. Department of Computer Sciences, University of Pisa, Corso Italia, 40, 56125, Pisa, Italy

    Ugo Montanari

  2. Center for Computer Sciences, University of Geneva, 24, Rue Général Dufour, 1211, Geneva 4, Switzerland

    José D. P. Rolim

  3. Department of Computer Sciences, ETH Zurich, 8092, Zurich, Switzerland

    Emo Welzl

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© 2000 Springer-Verlag Berlin Heidelberg

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Banderier, C., Flajolet, P., Schaeffer, G., Soria, M. (2000). Planar Maps and Airy Phenomena. In: Montanari, U., Rolim, J.D.P., Welzl, E. (eds) Automata, Languages and Programming. ICALP 2000. Lecture Notes in Computer Science, vol 1853. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-45022-X_33

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  • DOI: https://doi.org/10.1007/3-540-45022-X_33

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  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-67715-4

  • Online ISBN: 978-3-540-45022-1

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