Related papers: Black swans or dragon kings? A simple test for dev…
Large deviations for sums of i.i.d.\ random variables with stretched-exponential tails (also called Weibull or semi-exponential tails) have been well understood since the 60's, going back to Nagaev's seminal work. Many extensions in the…
We show that rain events are analogous to a variety of nonequilibrium relaxation processes in Nature such as earthquakes and avalanches. Analysis of high-resolution rain data reveals that power laws describe the number of rain events versus…
Experimental tests of Newton law put stringent constraints on potential deviations from standard theory with ranges from the millimeter to the size of planetary orbits. Windows however remain open for short range deviations, below the…
In the classical two-sample problem, the conventional approach for testing distributions equality is based on the difference between the two marginal empirical distribution functions, whereas a test for independence is based on the contrast…
Atomic interferometry can be used to probe dark energy models coupled to matter. We consider the constraints coming from recent experimental results on models generalising the inverse power law chameleons such as $f(R)$ gravity in the large…
Consider a network of M >> 1 nodes connected by N >> 1 links, in which the distribution of the number of links per node follows a power law with exponent 0<\alpha <1. The power law is naturally truncated due to the fact that N is finite. A…
The true nature of dark energy remains unclear: It is either a strange fluid in the Universe, with a negative effective pressure, or a breakdown in General Relativity on large scales. This question can only be answered through a suite of…
Strong anomalous diffusion is {often} characterized by a piecewise-linear spectrum of the moments of displacement. The spectrum is characterized by slopes $\xi$ and $\zeta$ for small and large moments, respectively, and by the critical…
Although living organisms are affected by many interrelated and unidentified variables, this complexity does not automatically impose a fundamental limitation on statistical inference. Nor need one invoke such complexity as an explanation…
We propose a simple way of testing whether a given set of observations can come from a given theoretical cumulative distribution. In the test more weight is attached to the tails of the distribution than in the usual Kolmogorov or Smirnov…
We propose a random walk model of asset returns where the parameters depend on market stress. Stress is measured by, e.g., the value of an implied volatility index. We show that model parameters including standard deviations and…
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…
We present a formalization of the well-known thesis that, in the case of independent identically distributed random variables $X_1,\dots,X_n$ with power-like tails of index $\alpha\in(0,2)$, large deviations of the sum $X_1+\dots+X_n$ are…
Power law is one of the the simplest forms of the relationship between different variables of a system. It leads naturally to the introduction of compound parameters describing physical properties of the system. Often one of the variables…
The size that an epidemic can reach, measured in terms of the number of fatalities, is an extremely relevant quantity. It has been recently claimed [Cirillo & Taleb, Nature Physics 2020] that the size distribution of major epidemics in…
We propose a model which explains how power-law crossover behaviour can arise in a system which is capable of experiencing cascading failure. In our model the susceptibility of the system to cascades is described by a single number, the…
We present an analysis of a devised sample of Rotation Curves (RCs), aimed at checking the consequences of a modified f(R) gravity on galactic scales. Originally motivated by the the dark energy mystery, this theory may serve as a…
We analyze a 19-year time series of North American electric power transmission system blackouts. Contrary to previously reported results we find a fatter than exponential decay in the distribution of inter-occurrence times and evidence of…
Given well-shuffled data, can we determine whether the data items are statistically (in)dependent? Formally, we consider the problem of testing whether a set of exchangeable random variables are independent. We will show that this is…
Branching and weak probabilistic bisimilarities are two well-known notions capturing behavioral equivalence between nondeterministic probabilistic systems. For probabilistic systems, divergence is of major concern. Recently several…