Critical scaling in standard biased random walks
| Autor: | Anteneodo, C., Morgado, W. A. M. |
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| Rok vydání: | 2008 |
| Předmět: | |
| Zdroj: | Phys. Rev. Lett. 99, 180602 (2007) |
| Druh dokumentu: | Working Paper |
| DOI: | 10.1103/PhysRevLett.99.180602 |
| Popis: | The spatial coverage produced by a single discrete-time random walk, with asymmetric jump probability $p\neq 1/2$ and non-uniform steps, moving on an infinite one-dimensional lattice is investigated. Analytical calculations are complemented with Monte Carlo simulations. We show that, for appropriate step sizes, the model displays a critical phenomenon, at $p=p_c$. Its scaling properties as well as the main features of the fragmented coverage occurring in the vicinity of the critical point are shown. In particular, in the limit $p\to p_c$, the distribution of fragment lengths is scale-free, with nontrivial exponents. Moreover, the spatial distribution of cracks (unvisited sites) defines a fractal set over the spanned interval. Thus, from the perspective of the covered territory, a very rich critical phenomenology is revealed in a simple one-dimensional standard model. Comment: 4 pages, 4 figures |
| Databáze: | arXiv |
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