Origin Of Power-law Distributions Research Articles

Emergence of power law distributions for odd and even lifetimes.

Avalanche lifetime distributions have been related to first-return random walk processes. In this sense, the theory for random walks can be employed to understand, for instance, the origin of power law distributions in self-organized criticality. In this work, we study first-return probability distributions, f^{(n)}, for discrete random walks with constant one-step transition probabilities. Explicit expressions are given in terms of _{2}F_{1} hypergeometric functions, allowing us to study the different behaviors of f^{(n)} for odd and even values of n. We show that the first-return probabilities have a power law behavior with exponent -3/2 only when the random walk is unbiased. In any other case, it presents an exponential decay.

Fractal Structure in Gauge Fields

In this work, we investigate fractal properties in Yang–Mills fields, in particular their Hausdorff fractal dimension. Fractal properties of quantum chromodynamics (QCD) have been suggested as the origin of power-law distributions in high energy collisions, as well as of non-extensive properties that have been observed experimentally. The fractal dimension obtained here can be calculated directly from the properties of the field theory.

Retraction: On the origin of power-law distributions in systems with constrained phase space [Condens. Matter Phys., 2013, vol. 16, 43802

Retraction: On the origin of power-law distributions in systems with constrained phase space [Condens. Matter Phys., 2013, vol. 16, 43802

On the origin of power-law distributions in systems with constrained phase space

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 superstatistical approach. The conditions at which the Shannon entropy functional leads to a power-law statistics are investigated. It is demonstrated that, from a quite general point of view, the power-law dependencies may appear as a consequence of "global" constraints restricting both the dynamic phase space and the stochastic fluctuations. As a result, at sufficiently long observation times, the dynamic counterpart is driven into a non-equilibrium steady state whose deviation from the usual exponential statistics is given by the distance from the conventional equilibrium.

Effect of Correlations on the Exponents for the Power-Law Distributions in Self-Organized Criticality

The origin of power-law distributions in self-organized criticality is investigated by treating the variation of the number of active sites in the system as a stochastic process. An avalanche is mapped to a first-return random-walk process in a one-dimensional lattice. In order to understand the reason of variant exponents for the power-law distributions in different self-organized critical systems, we introduce the correlations among evolution steps. Power-law distributions of the lifetime and spatial size are found when the random walk is unbiased with equal probability to move in opposite directions. It is found that the longer the correlation length, the smaller values of the exponents for the power-law distributions.

Exploring the origin of power law distribution in single-molecule conformation dynamics: Energy landscape perspectives

We explored the origin of power law distribution observed in single-molecule conformational dynamics experiments. By establishing a kinetic master equation approach to study statistically the microscopic state dynamics, we show that the underlying landscape with exponentially distributed density of states leads to power law distribution of kinetics. The exponential density of states emerges when the system becomes glassy and landscape becomes rough with significant trapping. We predicted the power law decay coefficient is monotonically dependent on temperature which can be tested from ongoing experiments. This work bridges statistics from single-molecule kinetic experiments and topography of conformational energy landscape.

On Origin of Power-Law Distributions in Self-Organized Criticality from Random Walk Treatment

The origin of power-law distributions in self-organized criticality is investigated by treating the variation of the number of active sites in the system as a stochastic process. An avalanche is then regarded as a first-return random walk process in a one-dimensional lattice. We assume that the variation of the number of active sites has three possibilities in each update: to increase by 1 with probability f1, to decrease by 1 with probability f2, or remain unchanged with probability 1-f1 -f2. This mimics the dynamics in the system. Power-law distributions of the lifetime are found when the random walk is unbiased with equal probability to move in opposite directions. This shows that power-law distributions in self-organized criticality may be caused by the balance of competitive interactions.

Origin of power-law distributions in deterministic walks: The influence of landscape geometry

We investigate the properties of a deterministic walk, whose locomotion rule is always to travel to the nearest site. Initially the sites are randomly distributed in a closed rectangular (ALxL) landscape and, once reached, they become unavailable for future visits. As expected, the walker step lengths present characteristic scales in one (L-->0) and two (AL approximately L) dimensions. However, we find scale invariance for an intermediate geometry, when the landscape is a thin striplike region. This result is induced geometrically by a dynamical trapping mechanism, leading to a power-law distribution for the step lengths. The relevance of our findings in broader contexts--of both deterministic and random walks--is also briefly discussed.

Limit order placement as an utility maximization problem and the origin of power law distribution of limit order prices

I consider the problem of the optimal limit order price of a financial asset in the framework of the maximization of the utility function of the investor. The analytical solution of the problem gives insight on the origin of the recently empirically observed power law distribution of limit order prices. In the framework of the model, the most likely proximate cause of this power law is a power law heterogeneity of traders' investment time horizons .

The origin of power-law distributions in self-organized criticality

The origin of power-law distributions in self-organized criticality is investigated by treating the variation of the number of active sites in the system as a stochastic process. An avalanche is then regarded as a first-return random walk process in a one-dimensional lattice. Power law distributions of the lifetime and spatial size are found when the random walk is unbiased with equal probability to move in opposite directions. This shows that power-law distributions in self-organized criticality may be caused by the balance of competitive interactions. At the mean time, the mean spatial size for avalanches with the same lifetime is found to increase in a power law with the lifetime.

A Possible Origin of Power-Law Distribution in Stock Markets

The origin of the power-law distribution in stock markets is discussed fromthe point of view of self-organized criticality. An analytical expression for thedistribution is given from a simple model consideration. We see that power-lawincreasing or decreasing distribution functions can have the same origin,depending on the values of the parameters.

Power laws in economics and finance: some ideas from physics

We discuss several models in order to shed light on the origin of power-law distributions and power-law correlations in financial time series. From an empirical point of view, the exponents describing the tails of the price increments distribution and the decay of the volatility correlations are rather robust and suggest universality. However, many of the models that appear naturally (for example, to account for the distribution of wealth) contain some multiplicative noise, which generically leads to non-universal exponents. Recent progress in the empirical study of the volatility suggests that the volatility results from some sort of multiplicative cascade. A convincing 'microscopic' (i.e. trader based) model that explains this observation is however not yet available. It would be particularly important to understand the relevance of the pseudo-geometric progression of natural human time scales on the long-range nature of the volatility correlations.

Power-laws in Economy and Finance: Some Ideas from Physics

We discuss several models in order to shed light on the origin of powerlaw distributions and power-law correlations in financial time series. From an empirical point of view, the exponents describing the tails of the price increments distribution and the decay of the volatility correlations are rather robust and suggest universality. However, many of the models that appear naturally (for example, to account for the distribution of wealth) contain some multiplicative noise, which generically leads to non universal exponents. Recent progress in the empirical study of the volatility suggests that the volatility results from some sort of multiplicative cascade. A convincing ‘microscopic’ (i.e. trader based) model that explains this observation is however not yet available. It would be particularly important to understand the relevance of the pseudo-geometric progression of natural human time scales on the long range nature of the volatility correlations.

Diffusion models of ion-channel gating and the origin of power-law distributions from single-channel recording.

The lifetimes of the unitary currents from ion channels, as revealed from single-channel recording, are traditionally thought to follow exponential or multiexponential distributions. The interpretation of these event-time distributions is that the gating process follows Markov kinetics among a small number of states. There is recent evidence, however, that certain systems exhibit distributions that follow power laws or functions related to power laws. Likewise, it has been suggested that data sets that appear to be multiexponential may be fit to simple power laws as well. In this paper we propose a different view of ion-channel-gating kinetics that is consistent with these recent experimental observations. We retain the Markovian nature of the kinetics, but, in contrast to the traditional models, we suggest that ion-channel proteins have a very large number of states all of similar energy. Gating, therefore, resembles a diffusion process. We show that our simplest one-dimensional model exhibits single-channel distributions that follow power laws of the form t-a, where 1/2 less than or equal to a less than or equal to 3/2. Exponents determined from recent experiments approximately fall within this range. We believe that this model is consistent with modern views of protein dynamics and, thus, may provide a key to the molecular details of the gating process.