We show that there is a common mode of origin for the power laws observed in two different models: (i) the Pareto law for the distribution of money among the agents with random-saving propensities in an ideal gas-like market model and (ii) the Gutenberg–Richter law for the distribution of...

We determine the geometrical properties of the most probable paths at finite temperatures T, between two points separated by a distance r, in one-dimensional lattices with positive energies of interaction εi associated with bond i. The most probable path-length tmp in a homogeneous medium...

A one-dimensional probabilistic cellular automaton that models a transition from elementary rule 4 to elementary rule 22 (following Wolfram's nomenclature scheme) is studied here. The evolution of the automaton follows rule 4 with probability 1 − p and rule 22 with probability p. In course of...

The characteristics of the distribution of transient times of a one-dimensional probabilistic cellular automaton are studied by computer simulation. The mean and width of the distribution are found to diverge by the same power-law at each of the two critical points, pc1 = 0 and pc2 0.75, of the...