It has been shown that, if a model displays long-range (power-law) spatial correlations, its equal-time correlation matrix will also have a power law tail in the distribution of its high-lying eigenvalues. The purpose of this paper is to show that the converse is generally incorrect: a power-law tail in the high-lying eigenvalues of the correlation matrix may exist even in the absence of equal-...

We present a simple explanation for the occurrence of power-law tails in statistical distributions by showing that if stochastic processes with exponential growth in expectation are killed (or observed) randomly, the distribution of the killed or observed state exhibits power-law behavior in one or both tails. This simple mechanism can explain power-law tails in the distributions of the sizes o...

We present a minimum hypothesis model for an IMF that resembles a lognormal distribution at low masses but has a distinct power-law tail. Even if the central limit theorem ensures a lognormal distribution of condensation masses at birth, a power-law tail in the distribution arises due to accretion from the ambient cloud, coupled with a non-uniform (exponential) distribution of accretion times. ...

Protein-protein interaction networks, particularly that of the yeast S. Cerevisiae, have recently been studied extensively. These networks seem to satisfy the small world property and their (1-hop) degree distribution seems to form a power law. More recently, a number of duplication based random graph models have been been proposed with the aim of emulating the evolution of protein-protein inte...

We show empirically a series of sharp patterns in stock market fluctuations, trading activity and their contemporaneous relationships. We link together and explain the following facts: (i) the cubic law of returns: returns follow a power law distribution with exponent 3. This “cubic” law seems to hold both across time and internationally. Stock market “crashes” (e.g. the 1929 and 1987 crashes) ...

This paper presents two new properties of BGP routes. First, it shows that the frequency of autonomous systems (ASs) appearing in path vectors follow a Power-Law relationship. Secondly, it shows that path lengths can be characterized accurately by stable distributions. The main implication of these properties is that it allows the creation of realistic forwarding tables for simulation studies. ...

– The probability distribution P (k) of the sizes k of critical trees (branching ratio m = 1) is well known to show a power-law behavior k. Such behavior corresponds to the mean-field approximation for many critical and self-organized critical phenomena. Here we show numerically and analytically that also supercritical trees (branching ration m > 1) are ”critical” in that their size distributio...

The distribution of seismic moment is of capital interest to evaluate earthquake hazard, in particular regarding the most extreme events. We make use of likelihood-ratio tests to compare the simple Gutenberg-Richter power-law (PL) distribution with two statistical models that incorporate an exponential tail, the so-called tapered Gutenberg-Richter (Tap) and the truncated gamma, when fitted to t...

We have derived a model of the Kuiper belt luminosity function exhibited by a broken power-law size distribution. This model allows direct comparison of the observed luminosity function to the underlying size distribution. We discuss the importance of the radial distribution model in determining the break diameter. We determine a best-fit break-diameter of the Kuiper belt size-distribution of 3...

Erosion and deposition rates estimated from the stratigraphic record frequently exhibit a power-law dependence on measurement interval. This dependence can result from a power-law distribution of stratigraphic hiatuses. By representing the stratigraphic filter as a stochastic process called a reverse ascending ladder, we describe a likely origin of power-law hiatuses, and thus, rate scaling. Wh...