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A strong negative dependence property for measures on {0,1}^n - stability -was recently developed in [5], by considering the zero set of the probabilitygenerating function. We extend this property to the more general setting ofreaction-diffusion processes and collections of independent Markov chains. Inone dimension the generalized stability property is now independentlyinteresting, and we characterize the birth-death chains preserving it.

Stability on {0,1,2,...}^S: birth-death chains and particle systems