Percolat ion on Fuchs ian groups
نویسندگان
چکیده
-It is shown that, for site percolation on the dual Dirichlet tiling graph of a co-compact Fuchsian group of genus > 2, infinitely many infinite connected clusters exist almost surely for certain values of the parameter p = P{site is open). In such cases, the set of limit points at oo of an infinite cluster is shown to be a perfect, nowhere dense set of Lebesgue measure 0. These results are also shown to hold for a class of hyperbolic triangle groups. © Elsevier, Pads R~UMI~.. -On montre que, pour la percolation de site sur le graphe de parage dual de Dirichlet d 'un groupe Fuchsien de genre > 2, il existe p.s. une infinit6 de composantes connexes infinies, pour certaines valeurs du param~tre p = P {(un site est ouvert)}. On montre dans ces cas que l 'ensemble des points limites ~t l'infini d 'une composante infinie est un ensemble parfait d'int6rieur vide de mesure de Lebesgue nulle. On obtient aussi ces r6sultats pour une classe de groupes triangulaires hyperboliques. © Elsevier, Pads
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تاریخ انتشار 2004