Related papers: A Dynamic Taylor's Law
The Taylor hypothesis which allows surrogating spatial measurements requiring many experimental probes by time series from one or two probes is examined on the basis of a simple analytic model of turbulent statistics. The main points are as…
A new model, called "Human Dynamics", has been recently proposed that individuals execute activities based on a perceived priority of tasks, which can be characterized by a power-law distribution of waiting time between consecutive tasks…
Several populational networks present complex topologies when implemented in evolutionary algorithms. A common feature of these topologies is the emergence of a power law. Power law behavior with different scaling factors can also be…
For taxonomic levels higher than species, the abundance distributions of number of subtaxa per taxon tend to approximate power laws, but often show strong deviationns from such a law. Previously, these deviations were attributed to…
Understanding the properties of response time distributions is a long-standing problem in cognitive science. We provide a tutorial overview of several contemporary models that assume power law scaling is a plausible description of the…
We study how the presence of correlations in physical variables contributes to the form of probability distributions. We investigate a process with correlations in the variance generated by (i) a Gaussian or (ii) a truncated L\'{e}vy…
Using population data of high spatial resolution for a region in the south of Europe, we define cities by aggregating individuals to form connected clusters. The resulting cluster-population distributions show a smooth decreasing behavior…
In the study of complex networks (systems), the scaling phenomenon of flow fluctuations refers to a certain power-law between the mean flux (activity) $<F_i>$ of the $i$th node and its variance $\sigma_i$ as $\sigma_i \propto < F_{i} >…
We consider a system of diffusing particles on the real line in a quadratic external potential and with repulsive electrostatic interaction. The empirical measure process is known to converge weakly to a deterministic measure-valued process…
Power law or generalized polynomial regressions with unknown real-valued exponents and coefficients, and weakly dependent errors, are considered for observations over time, space or space--time. Consistency and asymptotic normality of…
We analyze the asymptotic fluctuations of linear eigenvalue statistics of random centrosymmetric matrices with i.i.d. entries. We prove that for a complex analytic test function, the centered and normalized linear eigenvalue statistics of…
We study the evolution leading to (or regressing from) a large fluctuation in a Statistical Mechanical system. We introduce and study analytically a simple model of many identically and independently distributed microscopic variables $n_m$…
Proliferating cell populations at steady state growth often exhibit broad protein distributions with exponential tails. The sources of this variation and its universality are of much theoretical interest. Here we address the problem by…
We prove, for any $\beta >0$, a central limit theorem for the fluctuations of linear statistics in the Sine-$\beta$ process, which is the infinite volume limit of the random microscopic behavior in the bulk of one-dimensional log-gases at…
It is known (Hofmann-Credner and Stolz (2008)) that the convergence of the mean empirical spectral distribution of a sample covariance matrix W_n = 1/n Y_n Y_n^t to the Mar\v{c}enko-Pastur law remains unaffected if the rows and columns of…
A mass ejection model in a time-dependent random environment with both temporal and spatial correlations is introduced. When the environment has a finite correlation length, individual particle trajectories are found to diffuse at large…
We establish a central limit theorem for the fluctuations of the linear statistics in the $\beta$-ensemble of dimension $N$ at a temperature proportional to $N$ and with confining smooth potential. In this regime, the particles do not…
Models based on assumptions of multivariate regular variation and hidden regular variation provide ways to describe a broad range of extremal dependence structures when marginal distributions are heavy tailed. Multivariate regular variation…
This research paper talks about using complex mathematical tools to study and figure out the behavior of biological populations in porous media. Porous media offer a unique environment where various factors, including fluid flow and…
We derive a perturbation expansion for general self-interacting random walks, where steps are made on the basis of the history of the path. Examples of models where this expansion applies are reinforced random walk, excited random walk, the…