A lower bound on the two-arms exponent for critical percolation on the lattice

• Cerf, Raphaël ^[1]
  1. [1] University of Paris-Sud

     University of Paris-Sud

     Arrondissement de Palaiseau, Francia

     
• Localización: Annals of probability: An official journal of the Institute of Mathematical Statistics, ISSN 0091-1798, Vol. 43, Nº. 5, 2015, págs. 2458-2480
• Idioma: inglés
• DOI: 10.1214/14-AOP940
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• Resumen

  • We consider the standard site percolation model on the d-dimensional lattice. A direct consequence of the proof of the uniqueness of the infinite cluster of Aizenman, Kesten and Newman [Comm. Math. Phys. 111 (1987) 505–531] is that the two-arms exponent is larger than or equal to 1/2. We improve slightly this lower bound in any dimension d≥2. Next, starting only with the hypothesis that θ(p)>0, without using the slab technology, we derive a quantitative estimate establishing long-range order in a finite box.