Condensed Matter and Statistical Physics Journal Club
|Date:||February 11, 2008|
|Title:||Critical Scaling in Standard Biased Random Walks|
Based on the paper titled "Critical Scaling in Standard Biased Random Walks" by C. Anteneodo and W.A.M. Morgado [Phys.Rev.Lett.].
Abstract : "The spatial coverage produced by a single discrete-time random walk, with an asymmetric jump probability p ≠ 1/2 and nonuniform 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 = pc. Its scaling properties as well as the main features of the fragmented coverage occuring in the viscinity of the critical point are shown. In particular, in the limit p → pc, 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-dimensinal model."