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 μ reaches a critical value μc. For strong positive correlations, μ>μc, the survival probability is asymptotically finite, whereas for μ<μc it decays as a power law in time (chain length).
ASJC Scopus subject areas
- Statistical and Nonlinear Physics
- Statistics and Probability
- Condensed Matter Physics