Recently a uniqueness condition for Gibbs measures in terms of disagreement percolation (a type of dependent percolation involving two realizations) has been obtained. In general this condition is sufficient but not necessary for uniqueness. In the present paper we study the hard-core lattice...

We consider a linear sequence of 'nodes', each of which can be in state 0 ('off') or 1 ('on'). Signals from outside are sent to the rightmost node and travel instantaneously as far as possible to the left along nodes which are 'on'. These nodes are immediately switched off, and become on again...

Consider an ordinary Boolean model, that is, a homogeneous Poisson point process in Rd, where the points are all centres of random balls with i.i.d. radii. Now let these points move around according to i.i.d. stochastic processes. It is not hard to show that at each fixed time t we again have a...

We study versions of the contact process with three states, and with infections occurring at a rate depending on the overall infection density. Motivated by a model described in Kéfi et al. (2007) for vegetation patterns in arid landscapes, we focus on percolation under invariant measures of...