Related papers: A Master Equation for Power Laws
We propose a new formulation of stochastic thermodynamics for systems subjected to nonequilibrium constraints (i.e. broken detailed balance at steady state) and furthermore driven by external time-dependent forces. A splitting of the second…
One of the first steps to understand and forecast economic downturns is identifying their frequency distribution, but it remains uncertain. This problem is common in phenomena displaying power-law-like distributions. Power laws play a…
We study the dynamics of an intriguing crossover from a chaotic to a power law state as a function of strain rate within the context of a recently introduced model which reproduces the crossover. While the chaotic regime has a small set of…
We evaluate analytically and numerically the size of the frozen core and various scaling laws for critical Boolean networks that have a power-law in- and/or out-degree distribution. To this purpose, we generalize an efficient method that…
In this paper we study the macroscopic conduction properties of large but finite binary networks with conducting bonds. By taking a combination of a spectral and an averaging based approach we derive asymptotic formulae for the conduction…
The master equation and, more generally, Markov processes are routinely used as models for stochastic processes. They are often justified on the basis of randomization and coarse-graining assumptions. Here instead, we derive n-th order…
Power-law distributions are essential in computational and statistical investigations of extreme events and complex systems. The usual technique to generate power-law distributed data is to first infer the scale exponent $\alpha$ using the…
We develop a recursive method for perturbative solutions of the Fokker-Planck equation with nonlinear drift. The series expansion of the time-dependent probability density in terms of powers of the coupling constant is obtained by solving a…
We investigate fragmentation processes with a steady input of fragments. We find that the size distribution approaches a stationary form which exhibits a power law divergence in the small size limit, P(x) ~ x^{-3}. This algebraic behavior…
We propose a model which explains how power-law crossover behaviour can arise in a system which is capable of experiencing cascading failure. In our model the susceptibility of the system to cascades is described by a single number, the…
Consensus about the universality of the power law feature in complex networks is experiencing profound challenges. To shine fresh light on this controversy, we propose a generic theoretical framework in order to examine the power law…
Recently several authors have proposed stochastic evolutionary models for the growth of complex networks that give rise to power-law distributions. These models are based on the notion of preferential attachment leading to the ``rich get…
A practical statistical analysis on the regional populations and GDPs of China is conducted. The result shows that the distribution of the populations and that of the GDPs obeys the shifted power law, respectively. To understand these…
Behavior of condensed matter systems deviating from the standard equilibrium conditions is discussed. Statistical properties of coupled dynamic-stochastic systems are studied within a combination of the maximum information principle and the…
We perform a quantitative analysis of extensive chess databases and show that the frequencies of opening moves are distributed according to a power-law with an exponent that increases linearly with the game depth, whereas the pooled…
Power law distributions have been repeatedly observed in a wide variety of socioeconomic, biological and technological areas. In many of the observations, e.g., city populations and sizes of living organisms, the objects of interest evolve…
We introduce a stochastic model to explain a double power-law distribution which exhibits two different Paretian behaviors in the upper and the lower tail and widely exists in social and economic systems. The model incorporates fitness…
Carreras, Dobson and colleagues have studied empirical data on the sizes of the blackouts in real grids and modeled them by computer simulations using the direct current approximation. They have found that the resulting blackout sizes are…
We study the evolution of a particle system whose genealogy is given by a supercritical continuous time Galton--Watson tree. The particles move independently according to a Markov process and when a branching event occurs, the offspring…
Fokker-Planck equations (forward Kolmogorov equations) evolve probability densities in time from an initial condition. For distributions over the real line, these evolution equations can sometimes be transformed into dynamics over the…