Area distribution for directed random walks

Thordur Jonsson*, John F. Wheater

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

5 Citations (Scopus)


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.

Original languageEnglish
Pages (from-to)713-725
Number of pages13
JournalJournal of Statistical Physics
Issue number3-4
Publication statusPublished - Aug 1998

Other keywords

  • Directed random walks


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