Power Estimates

Abstract

In this chapter we study the behavior of the percolation probability and the expected size of an occupied cluster in a one-paremeter problem. As defined in Ch. 3 this means that we consider probability measures for which

$${{\text{P}}_{\text{p}}}\left\{ {{\text{v}}{\mkern 1mu} \,\,\,{\text{is}}\,{\mkern 1mu} {\text{occupied}}} \right\} = {\text{p}}$$

is the same for all vertices v of the studied graph G, and the occupancies of all vertices are independent.