Fixed scale transformation applied to fractal aggregation with levy flight particle trajectories

We extend the Fixed Scale Transformation (FST) method, developed for Laplacian fractal growth, to the case of aggregation phenomena based on diffusing particles following Levy-flight walk. We compute analytically the clusters fractal dimension for different values of the exponent governing the Levy-flight trajectories. The results obtained are in very good agreement with the numerical simulations and show analytically how the different screening effects present in the Levy-flight diffusion change the aggregates fractal dimension.