Related papers: Log-normal distribution in growing systems with we…
Analytical and numerical studies on many-body stochastic processes with multiplicative interactions are reviewed. The method of moment relations is used to investigate effects of asymmetry and randomness in interactions. Probability…
The logarithmic-normal (lognormal) distribution is one of the most frequently observed distributions in nature and describes a large number of physical, biological and even sociological phenomena. The origin of this distribution is…
We consider stochastic processes where randomly chosen particles with positive quantities x, y (> 0) interact and exchange the quantities asymmetrically by the rule x' = c{(1-a) x + b y}, y' = d{a x + (1-b) y} (x \ge y), where (0 \le) a, b…
A multiplicative stochastic process with the lower bound lognormally distributed is investigated. For the process, the model is constructed, and its distribution function (involving four parameters) and the related statistical properties…
Conventional Monte Carlo simulations are stochastic in the sense that the acceptance of a trial move is decided by comparing a computed acceptance probability with a random number, uniformly distributed between 0 and 1. Here we consider the…
The log-normal distribution is used to describe the positive data, that it has skewed distribution with small mean and large variance. This distribution has application in many sciences for example medicine, economics, biology and…
Random sequential adsorption of linear and square particles with excluded volume interaction is studied numerically on planar lattices considering Gaussian distributions of lateral sizes of the incident particles, with several values of the…
We consider a population of $N$ interacting neurons, represented by a multivariate Hawkes process: the firing rate of each neuron depends on the history of the connected neurons. Contrary to the mean-field framework where the interaction…
Mathematical models of motility are often based on random-walk descriptions of discrete individuals that can move according to certain rules. It is usually the case that large masses concentrated in small regions of space have a great…
In recent years it has been increasing evidence that lognormal distributions are widespread in physical and biological sciences, as well as in various phenomena of economics and social sciences. In social sciences, the appearance of…
The paper investigates the properties of a class of resource allocation algorithms for communication networks: if a node of this network has $x$ requests to transmit, then it receives a fraction of the capacity proportional to $\log(1+x)$,…
We present our recent work on stochastic particle systems on complex networks. As a noninteracting system we first consider the diffusive motion of a random walker on heterogeneous complex networks. We find that the random walker is…
Systems which consist of many localized constituents interacting with each other can be represented by complex networks. Consistently, network science has become highly popular in vast fields focusing on natural, artificial and social…
Normal variance mixtures are a class of multivariate distributions that generalize the multivariate normal by randomizing (or mixing) the covariance matrix via multiplication by a non-negative random variable W. The multivariate t…
We introduce a model of long-range interacting particles evolving under a stochastic Monte Carlo dynamics, in which possible increase or decrease in the values of the dynamical variables is accepted with preassigned probabilities. For…
Mathematical models of biological neural networks are associated to a rich and complex class of stochastic processes. In this paper, we consider a simple {\em plastic} neural network whose {\em connectivity/synaptic strength} $(W(t))$…
We analyze the full statistics of a stochastic squeeze process. The model's two parameters are the bare stretching rate~$w$, and the angular diffusion coefficient~$D$. We carry out an exact analysis to determine the drift and the diffusion…
We construct a model of wealth distribution, based on an interactive multiplicative stochastic process on static complex networks. Through numerical simulations we show that a decrease in the number of links discourages equality in wealth…
The statistical mechanics approach to wealth distribution is based on the conservative kinetic multi-agent model for money exchange, where the local interaction rule between the agents is analogous to the elastic particle scattering…
Gradually Truncated Log-normal distribution - Size distribution of firms Abstract Many natural and economical phenomena are described through power law or log- normal distributions. In these cases, probability decreases very slowly with…