  We study the decay of the probability for a non-Markovian stationary Gaussian
walker not to cross the origin up to time $t$. This result is 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.

Condensed Matter;Adaptation, Noise, and Self-Organizing Systems;Chaotic Dynamics;Adaptation and Self-Organizing Systems;Chaotic Dynamics;Pattern Formation and Solitons;Pattern Formation and Solitons