Analyticity Results in Bernoulli Percolation

Analyticity Results in Bernoulli Percolation Synopsis

"We prove that for Bernoulli percolation on Zd, d (greater than or equal to) 2, the percolation density is an analytic function of the parameter in the supercritical interval. For this we introduce some techniques that have further implications. In particular, we prove that the susceptibility is analytic in the subcritical interval for all transitive shortor long-range models, and that pbond c (less than) 1/2 for certain families of triangulations for which Benjamini & Schramm conjectured that psite c (less than or equal to) 1/2"--.