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.
Time-Dependent Random Walks and the Theory of Complex Adaptive Systems
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abstract
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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cond-mat.stat-mech 1years
2026 1verdicts
UNVERDICTED 1representative citing papers
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Quantitative description of cognitive fatigue in repetitive monotonous tasks
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.