Random Planar Lattices and Integrated SuperBrownian Excursion

Philippe Chassaing 1 Gilles Schaeffer 2
2 ADAGE - Applying discrete algorithms to genomics
INRIA Lorraine, LORIA - Laboratoire Lorrain de Recherche en Informatique et ses Applications
Abstract : In this extended abstract, a surprising connection is described between a specific brand of random lattices, namely planar quadrangulations, and Aldous' Integrated SuperBrownian Excursion (ISE). As a consequence, the radius r_n of a random quadrangulation with n faces is shown to converge, up to scaling, to the width r=R-L of the support of the one-dimensional ISE The combinatorial ingredients are an encoding by well labelled trees, reminiscent of the work of Cori and Vauquelin, and the conjugation of tree principle, used to relate the latter trees to embedded (discrete) plane trees in the sense of Aldous. {From} probability, we need a new result of independent interest, namely the weak convergence of the encoding of a random embedded plane tree by two contour walks (e^{(n)},\hat W^{(n)}) to the Brownian snake description (e,\hat W) of ISE.
Type de document :
Communication dans un congrès
Chauvin, B. and Flajolet, P., and Gardy, D. and Mokkadem, A. Colloquium on Mathematics and Computer Science: Algorithms, Trees, Combinatorics and Probabilities, Sep 2002, Versailles, France, Birkhauser, pp.123--141, 2002, Trends in Mathematics
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Soumis le : mardi 26 septembre 2006 - 09:08:30
Dernière modification le : jeudi 11 janvier 2018 - 06:19:48
Document(s) archivé(s) le : mercredi 29 mars 2017 - 12:36:25

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Philippe Chassaing, Gilles Schaeffer. Random Planar Lattices and Integrated SuperBrownian Excursion. Chauvin, B. and Flajolet, P., and Gardy, D. and Mokkadem, A. Colloquium on Mathematics and Computer Science: Algorithms, Trees, Combinatorics and Probabilities, Sep 2002, Versailles, France, Birkhauser, pp.123--141, 2002, Trends in Mathematics. 〈inria-00099448〉

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