Exact Meander Asymptotics: a Numerical Check

Philippe Di Francesco 1, Emmanuel Guitter 1, Jesper Lykke Jacobsen 2

Nuclear Physics B 580 (2000) 757-795

This note addresses the meander enumeration problem: \'Count all topologically inequivalent configurations of a closed planar non self-intersecting curve crossing a line through a given number of points\'. We review a description of meanders introduced recently in terms of the coupling to gravity of a two-flavored fully-packed loop model. The subsequent analytic predictions for various meandric configuration exponents are checked against exact enumeration, using a transfer matrix method, with an excellent agreement.

  • 1. Service de Physique Théorique (SPhT),
    CNRS : URA2306 – CEA : DSM/SPHT
  • 2. Laboratoire de Physique Théorique et Modèles Statistiques (LPTMS),
    CNRS : UMR8626 – Université Paris XI - Paris Sud