Related papers: Extreme Fluctuations in Small-Worlds with Relaxati…
We consider a broad class of Continuous Time Random Walks with large fluctuations effects in space and time distributions: a random walk with trapping, describing subdiffusion in disordered and glassy materials, and a L\'evy walk process,…
We study the steady state fluctuations of an Edwards-Wilkinson type surface with the substrate taken to be a sphere. We show that the height fluctuations on circles at a given latitude has the effective action of a perfect Gaussian $1/f$…
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…
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…
We revisit the gradient descent dynamics of the spherical Sherrington-Kirkpatrick ($p=2$) model with finite number of degrees of freedom. For fully random initial conditions we confirm that the relaxation takes place in three time regimes:…
In systems removed from equilibrium, intrinsic microscopic fluctuations become correlated over distances comparable to the characteristic macroscopic length over which the external constraint is exerted. In order to investigate this…
We study rare phase slips due to noise in synchronized Kuramoto oscillator networks. In the small-noise limit, we demonstrate that slips occur via large fluctuations to saddle phase-locked states. For tree topologies, slips appear between…
In this Letter, we investigate the stability of the statistical equilibrium of spherically symmetric collisionless self-gravitating systems. By calculating the second variation of the entropy, we find that perturbations of the relevant…
We study numerically the relaxation of a driven elastic string in a two dimensional pinning landscape. The relaxation of the string, initially flat, is governed by a growing length $L(t)$ separating the short steady-state equilibrated…
We present a new unified theory of critical finite-size scaling for lattice statistical mechanical models with periodic boundary conditions above the upper critical dimension. Our theory is based on recent mathematically rigorous results…
We study the role of finiteness and fluctuations about average quantities for basic structural properties of growing networks. We first determine the exact degree distribution of finite networks by generating function approaches. The…
Many natural systems show emergent phenomena at different scales, leading to scaling regimes with signatures of chaos at large scales and an apparently random behavior at small scales. These features are usually investigated quantitatively…
We present a thorough numerical analysis of the relaxational dynamics of the Sherrington-Kirkpatrick spherical model with an additive non-disordered perturbation for large but finite sizes $N$. In the thermodynamic limit and at low…
We introduce a class of stochastic weakly coupled map lattices, as models for studying heat conduction in solids. Each particle on the lattice evolves according to an internal dynamics that depends on its energy, and exchanges energy with…
Recent work has suggested that in highly correlated systems, such as sandpiles, turbulent fluids, ignited trees in forest fires and magnetization in a ferromagnet close to a critical point, the probability distribution of a global quantity…
We investigate whether enhanced gravitational scattering on small scales (< 0.1mm), which becomes possible in models with large extra dimensions, can establish statistical equilibrium between different particle species in the early…
Using the Anderson model for disordered systems the fluctuations in electron spectra near the metal--insulator transition were numerically calculated for lattices of sizes up to 28 x 28 x 28 sites. The results show a finite--size scaling of…
Recent work has shown that the synchronization process in lattices of self-sustained (phase and limit-cycle) oscillators displays universal scale-invariant behavior previously studied in the physics of surface kinetic roughening. The type…
We study analytically giant fluctuations and temporal intermittency in a stochastic one-dimensional model with diffusion and aggregation of masses in the bulk, along with influx of single particles and outflux of aggregates at the…
We study the distribution of the occurrence of rare patterns in sufficiently mixing Gibbs random fields on the lattice $\mathbb{Z}^d$, $d\geq 2$. A typical example is the high temperature Ising model. This distribution is shown to converge…