We introduce a simple model for the size distribution of avalanches based on
the idea that the front of an avalanche can be described by a directed random
walk. The model captures some of the qualitative features of earthquakes,
avalanches and other self-organized critical phenomena in one dimension. We
find scaling laws relating the frequency, size and width of avalanches and an
exponent 4/3 in the size distribution law.Comment: 16 pages Latex, macros included, 3 postscript figure