Journal of Statistical Physics, Vol. 36, Nos. 5/6, 1984, p. 909-916.
We discuss a model for the development of discharge patterns in dielectric breakdown based on the Laplace equation associated with a probability field. The model gives rise to random fractals with well-defined Hausdorff dimensions. The relations of this model with the diffusion-limited aggregation are discussed in detail. The possibility of application to other stochastic phenomena like fracture propagation is proposed.