Survival Probabilities of History-Dependent Random Walks

Details Survival Probabilities of History-Dependent Random Walks Survival Probabilities of History-Dependent Random Walks

2005-06-02

arxiv.org/abs/cond-mat/0506063v1

Phys. Rev. E 72, 046144 (2005)

Physics

Condensed Matter

Statistical Mechanics

3 pages, 2 figures

Scientific paper

10.1103/PhysRevE.72.046144

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).

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