Published online by Cambridge University Press: 01 July 2016
Conditioning independent and identically distributed bond percolation with retention parameter p on a one-dimensional periodic lattice on the event of having a bi-infinite path from -∞ to ∞ is shown to make sense, and the resulting model exhibits a Markovian structure that facilitates its analysis. Stochastic monotonicity in p turns out to fail in general for this model, but a weaker monotonicity property does hold: the average edge density is increasing in p.
Research supported by the Swedish Research Council.
Research supported by the Swedish Research Council and by the Göran Gustafsson Foundation for Research in the Natural Sciences and Medicine.