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

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

2002-12-03

arxiv.org/abs/cond-mat/0212055v1

Phys. Rev. Lett. {\bf 90}, 128701 (2003).

Physics

Condensed Matter

5 pages, 2 figures

Scientific paper

10.1103/PhysRevLett.90.128701

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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