Critical dynamics and global persistence in a probabilistic three-states cellular automaton

In this work a three-states cellular automaton proposed to describe part of a biological immune system is revisited. We obtain the dynamic critical exponent $z$ of the model by means of a recent technique that mixes different initial conditions. Moreover, by using two distinct approaches, we have also calculated the global persistence exponent $\theta_{g}$, related to the probability that the order parameter of the model does not change its sign up to time $t$ [$P(t)\propto t^{-\theta_{g}}$].