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Time-Dependent Random Walks and the Theory of Complex Adaptive Systems

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arxiv cond-mat/0212055 v1 pith:5W7USUJJ submitted 2002-12-03 cond-mat gr-qcnlin.AOnlin.SIphysics.bio-phphysics.data-anphysics.soc-ph

Shahar Hod This is my paper · ORCID
classification cond-matgr-qcnlin.AOnlin.SIphysics.bio-phphysics.data-anphysics.soc-ph
keywords jumpingprobabilityrandomabsorbingadaptiveboundarycomplexdynamics
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Motivated by novel results in the theory of complex adaptive systems, we analyze the dynamics of random walks in which the jumping probabilities are {\it time-dependent}. We determine the survival probability in the presence of an absorbing boundary. For an unbiased walk the survival probability is maximized in the case of large temporal oscillations in the jumping probabilities. On the other hand, a random walker who is drifted towards the absorbing boundary performs best with a constant jumping probability. We use the results to reveal the underlying dynamics responsible for the phenomenon of self-segregation and clustering observed in the evolutionary minority game.

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Cited by 2 Pith papers

Reviewed papers in the Pith corpus that reference this work. Sorted by Pith novelty score. Full citation record

  1. Survival probabilities in biased random walks: To restart or not to restart? that is the question

    cond-mat.stat-mech 2025-02 conditional novelty 5.0 of 10

    For a biased random walk with resetting to the start, the asymptotic survival probability exceeds that of an ordinary biased walker once the starting gap is above a critical value.

  2. Quantitative description of cognitive fatigue in repetitive monotonous tasks

    cond-mat.stat-mech 2026-06 unverdicted novelty 4.0 of 10

    In the Sisyphus random climb model the inverse-power-law form s(t) ~ t^{-1/N} separates success functions S(t) that approach 1 from those that approach a value strictly less than 1.

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