Deterministic and random partially self-avoiding walks in random media

✍ Scribed by César Augusto Sangaletti Terçariol; Rodrigo Silva González; Wilnice Tavares Reis Oliveira; Alexandre Souto Martinez

• Publisher: Elsevier Science
• Year: 2007
• Tongue: English
• Weight: 240 KB
• Volume: 386
• Category: Article
• ISSN: 0378-4371
• DOI: 10.1016/j.physa.2007.07.019

✦ Synopsis

Consider a set of N cities randomly distributed in the bulk of a hypercube with d dimensions. A walker, with memory m, begins his route from a given city of this map and moves, at each discrete time step, to the nearest point, which has not been visited in the preceding m steps. After reviewing the more interesting general results, we consider one-dimensional disordered media and show that the walker needs not to have full memory of its trajectory to explore the whole system, it suffices to have memory of order ln N= ln 2.