Related papers: Statistical description of domains in the Potts mo…
Heavy-tailed distributions are found throughout many naturally occurring phenomena. We have reviewed the models of stochastic dynamics that lead to heavy-tailed distributions (and power law distributions, in particular) including the…
The power law is useful in describing count phenomena such as network degrees and word frequencies. With a single parameter, it captures the main feature that the frequencies are linear on the log-log scale. Nevertheless, there have been…
The power-law distribution is ubiquitous and its mechanism seems to be various. We find a general mechanism for the distribution. The distribution of a geometrically growing system can be approximated by a log - completely squared chi…
We study the dynamics of protein folding via statistical energy-landscape theory. In particular, we concentrate on the local-connectivity case with the folding progress described by the fraction of native conformations. We obtain…
Although Zipf's law is widespread in natural and social data, one often encounters situations where one or both ends of the ranked data deviate from the power-law function. Previously we proposed the Beta rank function to improve the…
Zipf's law implies the statistical distributions of hyperbolic type, which can describe the properties of stability and entropy loss in linguistics. We present the information theory from which follows that if the system is described by…
This paper presents an extensive survey of regular distributions in natural and social sciences. The survey includes studies from a wide scope of academic disciplines, in order to create an inventory of the different mathematical functions…
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…
Using Monte Carlo simulations we study the phase ordering dynamics of a \textit{multi}-species system modeled via the prototype $q$-state Potts model. In such a \textit{multi}-species system, we identify a spin states or species as the…
Heavy-tailed phenomena appear across diverse domains --from wealth and firm sizes in economics to network traffic, biological systems, and physical processes-- characterized by the disproportionate influence of extreme values. These…
Zipf's law of city-size distributions can be expressed by three types of mathematical models: one-parameter form, two-parameter form, and three-parameter form. The one-parameter and one of the two-parameter models are familiar to urban…
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…
A numerical transfer matrix calculation is presented for two fully-frustrated three-state Potts models on the square lattice: the Potts piled-up-domino model and the Potts zig-zag model. The ground state entropies and phase diagrams are…
We investigate numerically and analytically Potts models on ``thin'' random graphs -- generic Feynman diagrams, using the idea that such models may be expressed as the N --> 1 limit of a matrix model. The thin random graphs in this limit…
The derivation of the maximum entropy distribution of particles in boxes yields two kinds of distributions: a "bell-like" distribution and a long-tail distribution. The first one is obtained when the ratio between particles and boxes is…
The spatial distribution of people exhibits clustering across a wide range of scales, from household ($\sim 10^{-2}$ km) to continental ($\sim 10^4$ km) scales. Empirical data indicates simple power-law scalings for the size distribution of…
Statistical properties of coupled dynamic-stochastic systems are studied within a combination of the maximum information principle and the superstatistical approach. The conditions at which the Shannon entropy functional leads to a…
Zipf's law states that the frequency of an observation with a given value is inversely proportional to the square of that value; Taylor's law, instead, describes the scaling between fluctuations in the size of a population and its mean.…
In a physical system, changing parameters such as temperature can induce a phase transition: an abrupt change from one state of matter to another. Analogous phenomena have recently been observed in large language models. Typically, the task…
We investigate Ising model description of dynamics of stock price. The model is defined in near 2 dimensions, one dimension is time and another represents ensemble of stocks, and strength of response of investors to price change corresponds…