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).
Keshet
Uri
U
Physics Faculty, Weizmann Institute, Rehovot 76100, Israel.
Hod
Shahar
S