title: Survival probabilities of history-dependent random walks.
abstract: 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).
authors.affiliation: Physics Faculty, Weizmann Institute, Rehovot 76100, Israel.
authors.forename: Uri
authors.initials: U
authors.lastname: Keshet
authors.forename: Shahar
authors.initials: S
authors.lastname: Hod