A local limit theorem for triple connections in subcritical Bernoulli   percolation
  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 $\mathbb{Z}^{d},\,d\geq2$ in the limit where their distances tend to infinity. 
Massimo Campanino, Michele Gianfelice
math.PR cond-mat.stat-mech math-ph math.MP