Nondifferentiability of the time constants of first-passage percolation

• J. Michael Steele ^[1] ; Yu Zhang ^[2]
  1. [1] University of Pennsylvania

     University of Pennsylvania

     City of Philadelphia, Estados Unidos

     
  2. [2] Colorado State University

     Colorado State University

     Estados Unidos

     
• Localización: Annals of probability: An official journal of the Institute of Mathematical Statistics, ISSN 0091-1798, Vol. 31, Nº. 2, 2003, págs. 1028-1051
• Idioma: inglés
• Texto completo no disponible (Saber más ...)
• Resumen

  • We study the paths of minimal cost for first-passage percolation in two dimensions and obtain an exponential bound on the tail probability of the ratio of the lengths of the shortest and longest of these. This inequality permits us to answer a long-standing question of Hammersley and Welsh on the shift differentiability of the time constant. Specifically, we show that for subcritical Bernoulli percolation the time constant is not shift differentiable when p is close to one-half.