Survival probabilities of history-dependent random walks

Uri Keshet; Shahar Hod

doi:10.1103/PhysRevE.72.046144

Survival probabilities of history-dependent random walks

Uri Keshet, Shahar Hod

Research output: Contribution to journal › Article › peer-review

14 Scopus citations

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).

Original language	English
Article number	046144
Journal	Physical Review E
Volume	72
Issue number	4
DOIs	https://doi.org/10.1103/PhysRevE.72.046144
State	Published - 1 Oct 2005
Externally published	Yes

ASJC Scopus subject areas

Statistical and Nonlinear Physics
Statistics and Probability
Condensed Matter Physics

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10.1103/PhysRevE.72.046144

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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 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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AB - 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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Survival probabilities of history-dependent random walks

Abstract

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