Requiring a generating function to have only real zeros has some nice probabilistic consequences, including a decomposition into iid Bernoulli variables which goes back to Levy. I'll describe a recent multivariate generalization of this restriction on zeros which leads to a strong negative dependence theory, and give applications to birth-death chains and a reaction-diffusion process. We will also see a universality result for non-equilibrium current flow in the symmetric exclusion process.