Related papers: A Generalized Preferential Attachment Model for Bu…
We study the rank distribution, the cumulative probability, and the probability density of returns of stock prices of listed firms traded in four stock markets. We find that the rank distribution and the cumulative probability of stock…
We address the issue of the distribution of firm size. To this end we propose a model of firms in a closed, conserved economy populated with zero-intelligence agents who continuously move from one firm to another. We then analyze the size…
We introduce a solvable model of randomly growing systems consisting of many independent subunits. Scaling relations and growth rate distributions in the limit of infinite subunits are analysed theoretically. Various types of scaling…
We propose and study a model of scale-free growing networks that gives a degree distribution dominated by a power-law behavior with a model-dependent, hence tunable, exponent. The model represents a hybrid of the growing networks based on…
A network growth mechanism based on a two-step preferential rule is investigated as a model of network growth in which no global knowledge of the network is required. In the first filtering step a subset of fixed size $m$ of existing nodes…
We propose a wide class of preferential attachment models of random graphs, generalizing previous approaches. Graphs described by these models obey the power-law degree distribution, with the exponent that can be controlled in the models.…
In this second part of our survey on the social and natural distributions, we investigate some models, which intend to explain the statistical regularity of the natural and social distributions. There is a large variety of models and in…
A version of ``preferential attachment'' random graphs, corresponding to linear ``weights'' with random ``edge additions,'' which generalizes some previously considered models, is studied. This graph model is embedded in a continuous-time…
We obtain closed form expressions for the expected conditional degree distribution and the joint degree distribution of the linear preferential attachment model for network growth in the steady state. We consider the multiple-destination…
We formalize a generalized form of the Pareto principle - ``fraction $p$ of inputs yields fraction $1-p$ of outputs'' - as a property of non-negative gain densities $\ell \in L^1([0,1])$, working with the decreasing rearrangement to obtain…
Zipf's law states that the number of firms with size greater than S is inversely proportional to S. Most explanations start with Gibrat's rule of proportional growth but require additional constraints. We show that Gibrat's rule, at all…
Urban agglomerations exhibit complex emergent features of which Zipf's law, i.e.\ a power-law size distribution, and fractality may be regarded as the most prominent ones. We propose a simplistic model for the generation of city-like…
Zipf's power law is a general empirical regularity found in many natural and social systems. A recently developed theory predicts that Zipf's law corresponds to systems that are growing according to a maximally sustainable path in the…
We propose a preferential attachment model for network growth where new entering nodes have a partial information about the state of the network. Our main result is that the presence of bounded information modifies the degree distribution…
The relationship between the size and the variance of firm growth rates is known to follow an approximate power-law behavior $\sigma(S) \sim S^{-\beta(S)}$ where $S$ is the firm size and $\beta(S)\approx 0.2$ is an exponent weakly dependent…
By employing exhaustive lists of large firms in European countries, we show that the upper-tail of the distribution of firm size can be fitted with a power-law (Pareto-Zipf law), and that in this region the growth rate of each firm is…
One of the best-known models in network science is preferential attachment. In this model, the probability of attaching to a node depends on the degree of all nodes in the population, and thus depends on global information. In many…
We introduce a random graph model based on k-trees, which can be generated by applying a probabilistic preferential attachment rule, but which also has a simple combinatorial description. We carry out a precise distributional analysis of…
This paper investigates the rank distribution, cumulative probability, and probability density of price returns for the stocks traded in the KSE and the KOSDAQ market. This research demonstrates that the rank distribution is consistent…
Zipf's power-law distribution is a generic empirical statistical regularity found in many complex systems. However, rather than universality with a single power-law exponent (equal to 1 for Zipf's law), there are many reported deviations…