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Survival Probabilities of History-Dependent Random Walks

Uri Keshet·Shahar Hod
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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 μreaches a critical value μ_c. For strong positive correlations, μ> μ_c, the survival probability is asymptotically finite, whereas for μ< μ_c it decays as a power-law in time (chain length).

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Uri Keshet, Shahar Hod. 2005-06-02. Survival Probabilities of History-Dependent Random Walks. https://doi.org/10.1103/physreve.72.046144

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