Related papers: Non-Normal Eigenvector Amplification in Multi-Dime…
We study the statistical fluctuations of Lyapunov exponents in the discrete version of the non-integrable perturbed sine-Gordon equation, the dissipative ac+dc driven Frenkel-Kontorova model. Our analysis shows that the fluctuations of the…
Detection of power-law behavior and studies of scaling exponents uncover the characteristics of complexity in many real world phenomena. The complexity of financial markets has always presented challenging issues and provided interesting…
In this paper we discuss the problem of the estimation of extreme event occurrence probability for data drawn from some multifractal process. We also study the heavy (power-law) tail behavior of probability density function associated with…
Motivated by the ubiquity of turbulent flows in realistic conditions, effects of turbulent advection on two models of classical non-linear systems are investigated. In particular, we analyze model A (according to the Hohenberg-Halperin…
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 $n_m$…
Perturbations in a non-normal system can grow transiently even if the system is linearly stable. If this transient growth is sufficiently large, it can trigger self-sustained oscillations from small initial disturbances. This has important…
We investigate the emergence of complex dynamics in networks with heavy-tailed connectivity by developing a non-Hermitian random matrix theory. We uncover the existence of an extended critical regime of spatially multifractal fluctuations…
Strong nonlinear effects combined with diffusive coupling may give rise to unpredictable evolution in spatially extended deterministic dynamical systems even in the presence of a fully negative spectrum of Lyapunov exponents. This regime,…
Stochastic quasi-cycles for a two species model of the excitatory-inhibitory type, arranged on a triangular loop, are studied. By increasing the strength of the inter-nodes coupling, one moves the system towards the Hopf bifurcation and the…
We consider a model for chaotic diffusion with amplification on graphs associated with piecewise-linear maps of the interval [S. Lepri, Chaos Solitons & Fractals, 139,110003 (2020)]. We determine the conditions for having fat-tailed…
Multiple types of fluctuations impact the collective dynamics of power grids and thus challenge their robust operation. Fluctuations result from processes as different as dynamically changing demands, energy trading, and an increasing share…
In this paper, we investigate the asymptotic behaviors of the extreme eigenvectors in a general spiked covariance matrix, where the dimension and sample size increase proportionally. We eliminate the restrictive assumption of the block…
In this paper, we investigate and develop a new approach to the numerical analysis and characterization of random fluctuations with heavy-tailed probability distribution function (PDF), such as turbulent heat flow and solar flare…
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…
[Takayasu et al., Phys. Rev.Lett. 79, 966 (1997)] revisited the question of stochastic processes with multiplicative noise, which have been studied in several different contexts over the past decades. We focus on the regime, found for a…
At high levels, the asymptotic distribution of a stationary, regularly varying Markov chain is conveniently given by its tail process. The latter takes the form of a geometric random walk, the increment distribution depending on the sign of…
We analyse a collection of empirical networks in a wide spectrum of disciplines and show that strong non-normality is ubiquitous in network science. Dynamical processes evolving on non-normal networks exhibit a peculiar behaviour, as…
We present a framework for describing the evolution of stochastic observables having a non-stationary distribution of values. The framework is applied to empirical volume-prices from assets traded at the New York stock exchange. Using…
We present results of the numerical simulations and the scaling characteristics of one-dimensional random fluctuations with heavy tailed probability distribution functions. Assuming that the distribution function of the random fluctuations…
We seek to quantify non-normality of the most amplified resolvent modes and predict their features based on the characteristics of the base or mean velocity profile. A 2-by-2 model linear Navier-Stokes (LNS) operator illustrates how…