Percolation in half-spaces: equality of critical densities and continuity of the percolation probability

Renormalization arguments are developed and applied to independent nearest-neighbor percolation on various subsets of ^d,d2, yielding:

–	Equality of the critical densities,pc(), for a half-space, quarter-space, etc., and (ford>2) equality with the limit of slab critical densities.
–	Continuity of the phase transition for the half-space, quarter-space, etc.; i.e., vanishing of the percolation probability,(p), atp=pc().

Corollaries of these results include uniqueness of the infinite cluster for such 's and sufficiency of the following for proving continuity of the full-space phase transition: showing that percolation in the full-space at densityp implies percolation in the half-space at thesame density.