Distributions exhibiting fat tails occur frequently in many different areas of science. A dynamical reason for fat tails can be a socalled superstatistics, where one has a superposition of local Gaussians whose variance fluctuates on a rather large spatio-temporal scale. After briefly reviewing this concept, we explore in more detail a class of superstatistics that hasn’t been subject of many i...

Power law distributions describe naturally-occurring events such as the magnitude of earthquakes, the diameter of moon craters or the complexity of the nervous system (Albert Lazslo Barabasi & Albert, 1999; Newman, 2005). Many man-made phenomena also tend to exhibit power law distributions, for example, the distribution of book titles sold, the sizes of cities or intensity of wars (Newman, 2005...

Power-law distributions are common, particularly in social physics. Here, we explore whether power-laws might arise as a consequence of a general variational principle for stochastic processes. We describe communities of ‘social particles’, where the cost of adding a particle to the community is shared equally between the particle joining the cluster and the particles that are already members o...

Power-law distributions have been a paradigm of complex systems for several decades. But it has been only recently that attention has been devoted to the proper fitting and goodness-of-fit testing of these distributions; in particular, Clauset et al.’s method is widely cited in this regard [1]. In the first part of the talk we present evidence that this method fails in some concrete examples of...

Many massive graphs (such as WWW graphs and Call graphs) share certain universal characteristics which can be described by socalled the “power law”. In this paper, we will first briefly survey the history and previous work on power law graphs. Then we will give four evolution models for generating power law graphs by adding one node/edge at a time. We will show that for any given edge density a...

Power law distributions are an increasingly common model for computer science applications; for example, they have been used to describe file size distributions and inand out-degree distributions for the Web and Internet graphs. Recently, the similar lognormal distribution has also been suggested as an appropriate alternative model for file size distributions. In this paper, we briefly survey s...

We present a simple explanation for the occurrence of power-law tails in statistical distributions by showing that if stochastic processes with exponential growth in expectation are killed (or observed) randomly, the distribution of the killed or observed state exhibits power-law behavior in one or both tails. This simple mechanism can explain power-law tails in the distributions of the sizes o...

We studied the mathematical relations between species abundance distributions (SADs) and species-area relationships (SARs) and found that a power-law SAR can be generally derived from a power-law SAD without a special assumption such as the “canonical hypothesis”. In the present analysis, an SAR-exponent is obtained as a function of an SAD-exponent for a finite number of species. We also studie...

It is generally recognized that economical systems, and more in general complex systems, are characterized by power law distributions. Sometime, these distributions show a changing of the slope in the tail so that, more appropriately, they show a multi-power law behavior. We present a method to derive analytically a two-power law distribution starting from a single power law function recently o...