Branching annihilating random walk on random regular graphs
The branching annihilating random walk is studied on a random graph whose sites have a uniform number of neighbors (z). The Monte Carlo simulations in agreement with the generalized mean-field analysis indicate that the concentration decreases linearly with the branching rate for z>/=4, while the coefficient of the linear term becomes zero if z=3. These properties are described by a modified mean-field theory taking explicitly into consideration the probability of mutual annihilation of the parent and its offspring particles using the returning features of a single walker on the same graph.
Szabo
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Research Institute for Technical Physics and Materials Science, P.O. Box 49, H-1525 Budapest, Hungary.