Time-Dependent Random Walks and the Theory of Complex Adaptive Systems
Condensed Matter
2016-08-31 v1 General Relativity and Quantum Cosmology
Adaptation and Self-Organizing Systems
Exactly Solvable and Integrable Systems
Biological Physics
Data Analysis, Statistics and Probability
Physics and Society
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.
Keywords
Cite
@article{arxiv.cond-mat/0212055,
title = {Time-Dependent Random Walks and the Theory of Complex Adaptive Systems},
author = {Shahar Hod},
journal= {arXiv preprint arXiv:cond-mat/0212055},
year = {2016}
}
Comments
5 pages, 2 figures