Related papers: Fluctuations and Pseudo Long Range Dependence in N…
This review article discusses limit distributions and variance bounds for particle current in several dynamical stochastic systems of particles on the one-dimensional integer lattice: independent particles, independent particles in a random…
Conjecture II.3.6 of Spohn in [Spohn '91] and Lecture 7 of Jensen-Yau in [Jensen-Yau '99] ask for a general derivation of universal fluctuations of hydrodynamic limits in large-scale stochastic interacting particle systems. However, the…
We consider diffusion processes on power-law small-world networks in different dimensions. In one dimension, we find a rich phase diagram, with different transient and recurrent phases, including a critical line with continuously varying…
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…
A Fluctuation Theorem (FT), both Classical and Quantum, describes the large-deviations in the approach to equilibrium of an isolated quasi-integrable system. Two characteristics make it unusual: (i) it concerns the internal dynamics of an…
We formulate multifractal models for velocity differences and gradients which describe the full range of length scales in turbulent flow, namely: laminar, dissipation, inertial, and stirring ranges. The models subsume existing models of…
In this paper we study the fluctuations from the limiting behavior of small noise random perturbations of diffusions with multiple scales. The result is then applied to the exit problem for multiscale diffusions, deriving the limiting law…
We investigate the dependence of river network scaling on the relative dominance of slope vs. noise in initial conditions, using an erosion model. Increasing slope causes network patterns to transition from dendritic to parallel and results…
We discuss a mechanism for the apparently universal scaling in the high-multiplicity tail of charged particle distributions for high energy nuclear collisions. We argue that this scaling behavior originates from rare fluctuations of the…
We investigate fluctuation phenomena for the graph distance and the number of cut points associated with random media arising from the range of a random walk. Our results demonstrate a sequence of dimension-dependent phase transitions in…
The Fluctuation Theorem (FT) gives an analytic expression for the probability, in a nonequilibrium system of finite size observed for a finite time, that the dissipative flux will flow in the reverse direction to that required by the Second…
We study diffusion with a bias towards a target node in networks. This problem is relevant to efficient routing strategies in emerging communication networks like optical networks. Bias is represented by a probability $p$ of the…
A stochastic model for intermittent fluctuations due to a super-position of uncorrelated Lorentzian pulses is presented. For constant pulse duration, this is shown to result in an exponential power spectral density for the stationary…
The scaling properties of the roughness of surfaces grown by two different processes randomly alternating in time, are addressed. The duration of each application of the two primary processes is assumed to be independently drawn from given…
Nonequilibrium complex systems are often effectively described by the mixture of different dynamics on different time scales. Superstatistics, which is "statistics of statistics" with two largely separated time scales, offers a consistent…
A stochastic model for intermittent fluctuations in the scrape-off layer of magnetically confined plasmas has been constructed based on a super-position of uncorrelated pulses arriving according to a Poisson process. In the most common…
In this article, we study transportation network in Minnesota. We show that the system is characterized by Taylor's power law for fluctuation scaling with nontrivial values of the scaling exponent. We also show that the characteristic…
In a class of heterogeneous random networks, where each node dynamics is a random dynamical system, interacting with neighbor nodes via a random coupling function, we characterize the hub behavior as the mean-field, subject to statistically…
In the standard cascade picture of 3D turbulent fluid flows, energy is input at a constant rate at large scales. Energy is then transferred to smaller scales by an intermittent process that has been the focus of a vast literature. However,…
We study the relation between flow structure and fluid deformation in steady two-dimensional random flows. Beyond the linear (shear flow) and exponential (chaotic flow) elongation paradigms, we find a broad spectrum of stretching behaviors,…