Postal address
Department of Theoretical Physics, Tata Institute of Fundamental Research, Homi Bhabha Road, Mumbai 400005, India.
Secretariat phones
+91-22-2278 2244 +91-22-2278 2777
+91-22-2280 4611 +91-22-2280 4610
Secretariat email
"theophys" The mailhost for DTP is


Condensed Matter and Statistical Physics Journal Club

Date: February 11, 2008
Title: Critical Scaling in Standard Biased Random Walks
Speaker: Kabir Ramola
Abstract: 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."