Survival Probability of a Gaussian Non-Markovian Process: Application to the T=0 Dynamics of the Ising Model

We study the decay of the probability for a non-Markovian stationary Gaussian walker not to cross the origin up to time $t$, using resummed perturbation theory and variational approach. These results are then used to evaluate the fraction of spins that do not flip up to time $t$ in the zero temperature Monte-Carlo spin flip dynamics of the Ising model. Our results are compared to extensive numerical simulations.