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.
Original language | English |
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Pages (from-to) | 713-725 |
Number of pages | 13 |
Journal | Journal of Statistical Physics |
Volume | 92 |
Issue number | 3-4 |
DOIs | |
Publication status | Published - Aug 1998 |
Other keywords
- Directed random walks