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Journal of Statistical Physics

, Volume 92, Issue 3–4, pp 713–725 | Cite as

Area Distribution for Directed Random Walks

  • Thordur Jonsson
  • John F. Wheater
Article

Abstract

We study the probability distribution for the area under a directed random walk in the plane. The walk can serve as a simple model for avalanches based on the idea that the front of an avalanche can be described by a random walk and the size is given by the area enclosed. This model captures some of the qualitative features of earthquakes, avalanches, and other self-organized critical phenomena in one dimension. By finding nonlinear functional relations for the generating functions we calculate directly the exponent in the size distribution law and find it to be 4/3.

Directed random walks 

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Copyright information

© Plenum Publishing Corporation 1998

Authors and Affiliations

  • Thordur Jonsson
    • 1
  • John F. Wheater
    • 1
  1. 1.Department of Theoretical PhysicsUniversity of OxfordOxfordUnited Kingdom

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