A spatial stochastic model for rumor transmission

We consider an interacting particle system representing the spread of a rumor by agents on the d-dimensional integer lattice. Each agent may be in any of the three states belonging to the set {0,1,2}. Here 0 stands for ignorants, 1 for spreaders and 2 for stiflers. A spreader tells the rumor to any of its (nearest) ignorant neighbors at rate lambda. At rate alpha a spreader becomes a stifler due to the action of other (nearest neighbor) spreaders. Finally, spreaders and stiflers forget the rumor at rate one. We study sufficient conditions under which the rumor either becomes extinct or survives with positive probability.

On Equilibrium Distribution of a Reversible Growth Model

We study a probabilistic model of interacting spins indexed by elements of a finite subset of the d-dimensional integer lattice, da parts per thousand yen1. Conditions of time reversibility are examined. It is shown that the model equilibrium distribution converges to a limit distribution as the indexing set expands to the whole lattice. The occupied site percolation problem is solved for the limit distribution. Two models with similar dynamics are also discussed.