It is shown that the use of the function ζ(r) for the analysis of statistical correlations for galaxies and clusters is conceptually incorrect. This is due to the fact that ζ(r) provides a correct characterization of correlations only for systems for which an intrinsic and unique average...

We consider a nonlinear version of the random β-model where the fragmentation probability of an eddy depends directly on the activity of the neighbouring regimes. We present an exact calculation for the complete multifractal spectrum. Inspired by concepts recently introduced in the theory of...

The impedance of a rough metal-electrolyte interface is known to show a complex impedance of type Z(ω) ∼ (iω)−gh at low frequencies. We study this problem for interfaces characterized by a self-similar fractal geometry. In contrast to previous theoretical studies we show that: (i) local...

We describe a new theoretical approach that clarifies the origin of fractal structures in irreversible growth models based on the Laplace equation and a stochastic field. This new theory provides a systematic method for the calculation of the fractal dimension D and of the multifractal spectrum...

Price dynamics is analyzed in terms of a model which includes the possibility of effective forces due to trend followers or trend adverse strategies. The method is tested on the data of a minority–majority model and indeed it is capable of reconstructing the prevailing traders’ strategies in...

The separation of the properties of the growth probability distribution in two different contributions, as discussed in the previous paper, corresponds naturally to the approximation scheme of the fixed scale transformation (FST) method. The growth probabilities used to compute the FST matrix...

We introduce a minimal Agent Based Model for financial markets to understand the nature and Self-Organization of the Stylized Facts. The model is minimal in the sense that we try to identify the essential ingredients to reproduce the main most important deviations of price time series from a...

Price dynamics is analyzed in terms of a model which includes the possibility of effective forces due to trend followers or trend adverse strategies. The method is tested on the data of a minority-majority model and indeed it is capable of reconstructing the prevailing traders' strategies in a...

We present a detailed analysis of the self-organization phenomenon in which the stylized facts originate from finite size effects with respect to the number of agents considered and disappear in the limit of an infinite population. By introducing the possibility that agents can enter or leave...

Suppose you look at today's stock prices and bet on the value of the first digit. One could guess that a fair bet should correspond to the frequency of $1/9 = 11.11%$ for each digit from 1 to 9. This is by no means the case, and one can easily observe a strong prevalence of the small values over...