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.