Related papers: Power Laws are Logarithmic Boltzmann Laws
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)…
A finite dimensional-system whose physics is governed by a Gaussian distribution can be regarded as a subsystem of an infinite dimensional-underlying system described by a uniform distribution on the (infinite dimensional) sphere. In turn,…
We consider a class of multiplicative processes which, added with stochastic reset events, give origin to stationary distributions with power-law tails -- ubiquitous in the statistics of social, economic, and ecological systems. Our main…
Unlike the classical exponential relaxation law, the widely prevailing universal law with its fractional power-law dependence of susceptibility on frequency cannot be explained in the framework of any intuitively simple physical concept.…
The central limit theorem ensures that a sum of random variables tends to a Gaussian distribution as their total number tends to infinity. However, for a class of positive random variables, we find that the sum tends faster to a log-normal…
For systems in nonequilibrium steady states, a novel modulated Gaussian probability distribution is derived to incorporate a new phenomenon of biased current fluctuations, discovered by recent laboratory experiments and confirmed by…
In branching process theory, linear-fractional distributions are commonly used to model individual reproduction, especially when the goal is to obtain more explicit formulas than those derived under general model assumptions. In this…
Many physical systems share the property of scale invariance. Most of them show ordinary power-law scaling, where quantities can be expressed as a leading power law times a scaling function which depends on scaling-invariant ratios of the…
Shift and stretch invariance lead to the exponential-Boltzmann probability distribution. Rotational invariance generates the Gaussian distribution. Particular scaling relations transform the canonical exponential and Gaussian patterns into…
Protein concentration in a living cell fluctuates over time due to noise in growth and division processes. From extensive single-cell experiments by using E. coli strains with different promoter strength (over two orders of magnitude) and…
Random multiplicative processes $w_t =\lambda_1 \lambda_2 ... \lambda_t$ (with < \lambda_j > 0 ) lead, in the presence of a boundary constraint, to a distribution $P(w_t)$ in the form of a power law $w_t^{-(1+\mu)}$. We provide a simple and…
We propose a new mechanism for generating power laws. Starting from a random walk, we first outline a simple derivation of the Fokker-Planck equation. By analogy, starting from a certain Markov chain, we derive a master equation for power…
We construct "stochastic mappings" between power law probability distributions (PD's) and Gaussian ones. To a given vector $N$, Gaussian distributed (respectively $Z$, exponentially distributed), one can associate a vector $X$, "power law…
We introduce a non-growth model that generates the power-law distribution with the Zipf exponent. There are N elements, each of which is characterized by a quantity, and at each time step these quantities are redistributed through binary…
We study the emergence of a power law distribution in the systems which can be characterized by a hierarchically organized supplying network. It is shown that conservation laws on the branches of the network can, at some approximation,…
We analyze the probabilities of large infrequent fluctuations in systems driven by external fields. In a broad range of the field magnitudes, the logarithm of the fluctuation probability is linear in the field magnitude, and the response…
In the last decade, stochastic models have shown to be very useful for quantitative modelling of social processes. Here, a configurational master equation for the description of behavioral changes by pair interactions of individuals is…
A growing body of theoretical and empirical evidence shows that the global steady-state distributions of many equilibrium and nonequilibrium systems approximately satisfy an analogue of the Boltzmann distribution, with a local dynamical…
Natural language data follows a power-law distribution, with most knowledge and skills appearing at very low frequency. While a common intuition suggests that reweighting or curating data towards a uniform distribution may help models…
A class of conserved models of wealth distributions are studied where wealth (or money) is assumed to be exchanged between a pair of agents in a population like the elastically colliding molecules of a gas exchanging energy. All sorts of…