Survival and Percolation Probabilities in the Field Theory of Growth Models

TL;DR

This paper develops a field theoretical framework for calculating survival and percolation probabilities in growth models with spreading, emphasizing the role of absorbing noise and critical scaling properties.

Contribution

It introduces feasible perturbation expansion expressions for these probabilities and discusses their critical behavior across universality classes.

Findings

Field theoretical expressions for survival and percolation probabilities

Monotonic decrease of survival probabilities over time

Critical scaling properties of probabilities

Abstract

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 to obtain survival probabilities monotonic 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 and probabilities are stated. In an appendix we consider shortly the renormalized field theory of compact directed percolation.