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 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).
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