Survival and percolation probabilities in the field theory of growth models

Survival and percolation probabilities are most important quantities in the theory and in the application of growth models with spreading. We construct field theoretical expressions for these probabilities which are feasible for perturbation expansions. The outstanding role of the absorbing noise is stressed in obtaining survival probabilities monotonically decreasing with time. We briefly consider some fundamental growth models equipped with absorbing noise which are representations of known universality classes of spreading phenomena. The critical scaling properties of their survival and percolation probabilities are stated. In an appendix we consider briefly the renormalized field theory of compact directed percolation.