Distances in the highly supercritical percolation cluster

• Anne-Laure Basdevant ^[1] ; Nathanaël Enriquez ^[1] ; Lucas Gerin ^[1]
  1. [1] Paris West University Nanterre La Défense

     Paris West University Nanterre La Défense

     París, Francia

     
• Localización: Annals of probability: An official journal of the Institute of Mathematical Statistics, ISSN 0091-1798, Vol. 41, Nº. 6, 2013, págs. 4342-4358
• Idioma: inglés
• DOI: 10.1214/12-AOP802
• Texto completo no disponible (Saber más ...)
• Resumen

  • On the supercritical percolation cluster with parameter p, the distances between two distant points of the axis are asymptotically increased by a factor 1+1−p2+o(1−p) with respect to the usual distance. The proof is based on an apparently new connection with the TASEP (totally asymmetric simple exclusion process).