Related papers: Extreme Fluctuations in Small-Worlds with Relaxati…
Extreme value statistics, or extreme statistics for short, refers to the statistics that characterizes rare events of either unusually high or low intensity: climate disasters like floods following extremely intense rains are among the…
We develop stochastic mixed finite element methods for spatially adaptive simulations of fluid-structure interactions when subject to thermal fluctuations. To account for thermal fluctuations, we introduce a discrete fluctuation-dissipation…
A two-dimensional lattice system of non-interacting electrons in a homogeneous magnetic field with half a flux quantum per plaquette and a random potential is considered. For the large scale behavior a supersymmetric theory with collective…
A pair of flat parallel surfaces, each freely diffusing along the direction of their separation, will eventually come into contact. If the shapes of these surfaces also fluctuate, then contact will occur when their centers of mass remain…
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…
We study the invariant measures and fluctuation limits of discrete-time harness processes in one spatial dimension. We construct one essential ergodic (under spatial shifts) invariant measure of the increment process derived from harness…
The article reviews recent developments in the theory of fluctuations and correlations of energy levels and eigenfunction amplitudes in diffusive mesoscopic samples. Various spatial geometries are considered, with emphasis on…
We consider the limiting behavior of fluctuations of small noise diffusions with multiple scales around their homogenized deterministic limit. We allow full dependence of the coefficients on the slow and fast motion. These processes arise…
Recently, Watts and Strogatz introduced the so-called small-world networks in order to describe systems which combine simultaneously properties of regular and of random lattices. In this work we study diffusion processes defined on such…
The frequency and magnitude of weather extreme events have increased significantly during the past few years in response to anthropogenic climate change. However, global statistical characteristics and underlying physical mechanisms are…
Extreme environmental events such as severe storms, drought, heat waves, flash floods, and abrupt species collapse have become more prevalent in the earth-atmosphere dynamic system in recent years. In order to fully understand the…
In one dimension very general results from conformal field theory and exact calculations for certain quantum spin systems have established universal scaling properties of the entanglement entropy between two parts of a critical system.…
Diffusion on a T fractal lattice under the influence of topological biasing fields is studied by finite size scaling methods. This allows to avoid proliferation and singularities which would arise in a renormalization group approach on…
Classically chaotic systems relax to coarse grained states of equilibrium. Here we numerically study the quantization of such bounded relaxing systems, in particular the quasi-periodic fluctuations associated with the correlation between…
We report on the exact treatment of a random-matrix representation of bond percolation model on a square lattice in two dimensions with occupation probability $p$. The percolation problem is mapped onto a random complex matrix composed of…
When two isolated system are brought in contact, they relax to equilibrium via energy exchange. In another setting, when one of the systems is driven and the other is large, the first system reaches a steady-state which is not described by…
We study a discrete model of an heterogeneous elastic line with internal disorder, submitted to thermal fluctuations. The monomers are connected through random springs with independent and identically distributed elastic constants drawn…
We explain how the statistics of global observables in correlated systems can be related to extreme value problems and to Gumbel statistics. This relationship then naturally leads to the emergence of the generalized Gumbel distribution…
The structure of very complicated irregular "microscopic" (local) entropy fluctuations around a big separated "macroscopic" (global) fluctuation in the statistical equilibrium was studied in numerical experiments on a simple 2--freedom…
We consider interacting many particle systems with quenched disorder having strong Griffiths singularities, which are characterized by the dynamical exponent, z, such as random quantum systems and exclusion processes. In several d=1 and d=2…