The distribution of first digits in numbers series obtained from very different origins shows a marked asymmetry in favor of small digits that goes under the name of Benford's law. We analyze in detail this property for different data sets and give a general explanation for the origin of the...

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...

The problem of classical diffusion in a random medium is mapped into a quantum mechanical problem with a disordered potential, and the dependence of the localization properties of the ground state wave function on the space dimensionality is analyzed. An extended ground state is obtained for D ...