Related papers: A Dynamic Taylor's Law
We study the linear eigenvalue statistics of large random graphs in the regimes when the mean number of edges for each vertex tends to infinity. We prove that for a rather wide class of test functions the fluctuations of linear eigenvalue…
We investigate the relevance of {\sl self-organized criticality (SOC)} models in previously published empirical datasets, which includes statistical observations in astrophysics, geophysics, biophysics, sociophysics, and informatics. We…
In this work, we obtain the central limit theorem for fluctuations of Young diagrams around their limit shape in the bulk of the "spectrum" of partitions of a large integer n (under the Plancherel measure). More specifically, we show that,…
We prove Taylor scaling for dislocation lines characterized by line-tension and moving by curvature under the action of an applied shear stress in a plane containing a random array of obstacles. Specifically, we show--in the sense of…
In this paper, we establish the central limit theorem (CLT) for linear spectral statistics (LSS) of large-dimensional sample covariance matrix when the population covariance matrices are not uniformly bounded, which is a nontrivial…
We study the number of occurrences of any fixed vincular permutation pattern. We show that this statistics on uniform random permutations is asymptotically normal and describe the speed of convergence. To prove this central limit theorem,…
We study a few dynamical systems composed of many components whose sizes evolve according to multiplicative stochastic rules. We compare them with respect to the emergence of power laws in the size distribution of their components. We show…
We revisit the classical population genetics model of a population evolving under multiplicative selection, mutation and drift. The number of beneficial alleles in a multi-locus system can be considered a trait under exponential selection.…
We perform an experimental study of the time behavior of the $\alpha$-wave events occuring in human electroencephalographic signals. We find that the fraction of the time spent in an $\alpha$-burst of time size $\tau$ exhibits a scaling…
We propose a model of random diffusion to investigate flow fluctuations in complex networks. We derive an analytical law showing that the dependence of fluctuations with the mean traffic in a network is ruled by the delicate interplay of…
Stochastic simulations are used to create synthetic one-dimensional telegraph approximation (TA) signals based on turbulent zero crossings, where the interval between crossings is governed by a power law probability distribution with…
Citation averages, and Impact Factors (IFs) in particular, are sensitive to sample size. We apply the Central Limit Theorem (CLT) to IFs to understand their scale-dependent behavior. For a journal of $n$ randomly selected papers from a…
Using a sensitive statistical test we determine whether or not one can detect the breakdown of linear response given observations of deterministic dynamical systems. A goodness-of-fit statistics is developed for a linear statistical model…
The dynamics of adaptation is difficult to predict because it is highly stochastic even in large populations. The uncertainty emerges from number fluctuations, called genetic drift, arising in the small number of particularly fit…
Financial time series typically exhibit strong fluctuations that cannot be described by a Gaussian distribution. In recent empirical studies of stock market indices it was examined whether the distribution P(r) of returns r(tau) after some…
Using numerical simulations and scaling theory we study the dynamics of the world-wide Web from the growth rules recently proposed in Ref. [1] with appropriate parameters. We demonstrate that the emergence of power-law behavior of the out-…
We revisit the problem of influencing the sex ratio of a population by subjecting reproduction of each family to some stopping rule. As an easy consequence of the strong law of large numbers, no such modification is possible in the sense…
We study the time evolution of Solar Flares activity by looking at the statistics of quiescent times $\tau_{L}$ between successive bursts. The analysis of 20 years of data reveals a power law distribution with exponent $\alpha \simeq 2.4$…
Motivated by the previous results by Coletti-de Lima-Gava-Luiz (2020) and Shiozawa (2022), we study the fluctuation of the dynamic elephant random walk in the superdiffusive case with a strong elephant component. Applying the martingale…
Population dynamics deals with the collective phenomena of living organisms, and it has attracted much attention since it is expected to explain how not only living organisms but also human beings have been adapted to varying environments.…