A local limit theorem for triple connections in subcritical Bernoulli percolation

Abstract

We prove a local limit theorem for the probability of a site to be connected by disjoint paths to three points in subcritical Bernoulli percolation on ${\mathbb{Z}}^d,d\ge 2$ in the limit where their distances tend to infinity.

31 pages

References in corpus (2)

• Ornstein-Zernike Theory for the finite range Ising models above T_c
• Rigorous Non-Perturbative Ornstein-Zernike Theory for Ising Ferromagnets

Cited by in corpus (3)

• On the Gibbs states of the noncritical Potts model on Z^2
• Entropic repulsion and scaling limit for a finite number of non-intersecting subcritical FK interfaces
• Ornstein-Zernike behavior for Ising models with infinite-range interactions