CROSSOVER TO GAUSSIAN BEHAVIOR IN HERDING MARKET MODELS

We have analyzed possible mechanisms of the crossover to the Gaussian distribution of the logarithmic returns in the Cont–Bouchaud herding model of the stock market. Either the underlying cluster distribution is not in the Lévy attraction regime, or a cut-off effect is responsible for the crossover. The cut-off can be due to the finite size of the system, where clusters are created. If such finite size effects are responsible for the crossover, a delicate interplay between the size dependence of the deviation from the Gaussian and of the number of values to be summed up in one step may result in a size-independent crossover value of the activity. It is shown that this is the case for percolation clusters in spatial dimensions from 2 to 6. A further origin of the cut-off can be the limited number of clusters taken into account.