Time-Dependent Random Walks and the Theory of Complex Adaptive Systems
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 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.
- Publication:
-
Physical Review Letters
- Pub Date:
- March 2003
- DOI:
- 10.1103/PhysRevLett.90.128701
- arXiv:
- arXiv:cond-mat/0212055
- Bibcode:
- 2003PhRvL..90l8701H
- Keywords:
-
- 02.50.Le;
- 05.40.Fb;
- 87.23.Kg;
- Decision theory and game theory;
- Random walks and Levy flights;
- Dynamics of evolution;
- Condensed Matter;
- General Relativity and Quantum Cosmology;
- Nonlinear Sciences - Adaptation and Self-Organizing Systems;
- Nonlinear Sciences - Exactly Solvable and Integrable Systems;
- Physics - Biological Physics;
- Physics - Data Analysis;
- Statistics and Probability;
- Physics - Physics and Society
- E-Print:
- 5 pages, 2 figures