Related papers: A Dynamic Taylor's Law
A collection of $N$-diffusing interacting particles where each particle belongs to one of $K$ different populations is considered. Evolution equation for a particle from population $k$ depends on the $K$ empirical measures of particle…
A general multi-type population model is considered, where individuals live and reproduce according to their age and type, but also under the influence of the size and composition of the entire population. We describe the dynamics of the…
In this paper, we study the dynamics of a linear control system with given state feedback control law in the presence of fast periodic sampling at temporal frequency $1/\delta$ ($0 < \delta \ll 1$), together with small white noise…
One of the first steps to understand and forecast economic downturns is identifying their frequency distribution, but it remains uncertain. This problem is common in phenomena displaying power-law-like distributions. Power laws play a…
Recent work in dynamic causal inference introduced a class of discrete-time stochastic processes that generalize martingale difference sequences and arrays as follows: the random variates in each sequence have expectation zero given certain…
This paper introduces nonparametric econometric methods that characterize general power law distributions under basic stability conditions. These methods extend the literature on power laws in the social sciences in several directions.…
We derive a central limit theorem for a spatial $\Lambda$-Fleming-Viot model with fluctuating population size. At each reproduction, a proportion of the population dies and is replaced by a not necessarily equal mass of new individuals. The…
Many applications of contemporary science involve multiscale dynamics, which are typically characterized by the time and space scale separation of patterns of motion, with fewer slowly evolving variables and much larger set of faster…
For a fixed positive integer $\;k,\;$ limit laws of linearly normalized $\;k$-th upper order statistics are well known. In this article, a comprehensive study of tail behaviours of limit laws of normalized $k$-th upper order statistics…
The Central Limit Theorem provides a foundation for inferential statistics and hypothesis testing. It describes how standardized statistics behave under repeated sampling from large populations. However, if the size of the sample (n)…
Using demographic data of high spatial resolution for a region in the south of Europe, we study the population over fixed-size spatial cells. We find that, counterintuitively, the distribution of the number of inhabitants per cell increases…
This paper discusses fluctuations of linear spectral statistics of high-dimensional sample covariance matrices when the underlying population follows an elliptical distribution. Such population often possesses high order correlations among…
In this article, we revisit the question of fluctuations of linear statistics of beta ensembles in the single cut and non-critical regime for general potentials $V$ under mild regularity and growth assumptions. Our main objective is to…
This article is a presentation of specific recent results describing scaling limits of individual-based models. Thanks to them, we wish to relate the time-scales typical of demographic dynamics and natural selection to the parameters of the…
We found that models of evolving random networks exhibit dynamic scaling similar to scaling of growing surfaces. It is demonstrated by numerical simulations of two variants of the model in which nodes are added as well as removed [Phys.…
We extend a generic class of systems which have previously been shown to spontaneously develop scaling (power law) distributions of their elementary degrees of freedom. While the previous systems were linear and exploded exponentially for…
A generic model of stochastic autocatalytic dynamics with many degrees of freedom $w_i$ $i=1,...,N$ is studied using computer simulations. The time evolution of the $w_i$'s combines a random multiplicative dynamics $w_i(t+1) = \lambda…
A mapping of nonextensive statistical mechanics into Gibbs' statistical mechanics exists, which leads to a generalization of Einstein's formula for fluctuations. A unified treatment of stability of relaxed states in nonextensive statistical…
This paper addresses the following classical question: giving a sequence of identically distributed random variables in the domain of attraction of a normal law, does the associated linear process satisfy the central limit theorem? We study…
Scaling laws in ecology, intended both as functional relationships among ecologically-relevant quantities and the probability distributions that characterize their occurrence, have long attracted the interest of empiricists and…