Stability on {0, 1, 2, …}S: Birth-Death Chains and Particle Systems

@article{Liggett2011StabilityO,
  title={Stability on \{0, 1, 2, …\}S: Birth-Death Chains and Particle Systems},
  author={T. Liggett and A. Vandenberg-Rodes},
  journal={arXiv: Probability},
  year={2011},
  pages={311-329}
}
A strong negative dependence property for measures on {0, 1} n - stability - was recently developed in [5], by considering the zero set of the probability generating function. We extend this property to the more general setting of reaction-diffusion processes and collections of independent Markov chains. In one dimension the generalized stability property is now independently interesting, and we characterize the birth-death chains preserving it. 
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