Survival probabilities of history-dependent random walks

We analyze the dynamics of random walks with long-term memory (binary chains with long-range correlations) in the presence of an absorbing boundary. An analytically solvable model is presented, in which a dynamical phase transition occurs when the correlation strength parameter mu reaches a critical value mu(c). For strong positive correlations, mu >mu(c), the survival probability is asymptotically finite, whereas for mu <mu(c) it decays as a power law in time (chain length).