Related papers: Non-equilibrium Fluctuations of the Weakly Asymmet…
Statistical inference for non-stationary data is hindered by the failure of classical central limit theorems (CLTs), not least because there is no fixed Gaussian limit to converge to. To resolve this, we introduce relative weak convergence,…
Fluctuations of the atomic positions are at the core of a large class of unusual material properties ranging from quantum para-electricity to high temperature superconductivity. Their measurement in solids is the subject of an intense…
We review generalized Fluctuation-Dissipation Relations which are valid under general conditions even in ``non-standard systems'', e.g. out of equilibrium and/or without a Hamiltonian structure. The response functions can be expressed in…
Small thermodynamic systems exhibit peculiar behavior different from that observed in long-scale systems. Non-equilibrium processes taking place in those systems are strongly influenced by the presence of fluctuations which can be large.…
Fluctuation relations establish rigorous identities for the nonequilibrium averages of observables. Starting from a general transport master equation with time-dependent rates, we employ the stochastic path integral approach to study…
We present a new description of nonequilibrium square patterns as a harmonically coupled crystal lattice. In a vertically oscillating granular layer, different transverse normal modes of the granular square-lattice pattern are observed for…
The study of discrete-time stochastic processes on the half-line with mean drift at $x$ given by $\mu_1 (x) \to 0$ as $x \to \infty$ is known as Lamperti's problem. We give sharp almost-sure bounds for processes of this type in the case…
This note proves an upper bound for the fluctuations of a second-class particle in the totally asymmetric simple exclusion process. The proof needs a lower tail estimate for the last-passage growth model associated with the exclusion…
We study the weak coupling limit of the Anderson Hamiltonian in the critical dimension $d=4$. In a perturbative sense, we prove Gaussian fluctuations about the Green's function of the Laplacian. The fluctuations are described by an explicit…
The fluctuation theorem is the fundamental equality in nonequilibrium thermodynamics that is used to derive many important thermodynamic relations, such as the second law of thermodynamics and the Jarzynski equality. Recently, the…
A wide range of disordered materials contain electronic states that are spatially well localized. In this work, we investigated the electrical response of such systems in non-equilibrium conditions to external electromagnetic field. We…
We investigate the impacts of combination of fermion-fermion interactions and impurity scatterings on the low-energy stabilities of two-dimensional asymmetric materials with a quadratic band crossing point by virtue of the renormalization…
We develop a non-equilibrium theory to describe weak Coulomb blockade effects in open quantum dots. Working within the bosonized description of electrons in the point contacts, we expose deficiencies in earlier applications of this method,…
A finite range interacting particle system on a transitive graph is considered. Assuming that the dynamics and the initial measure are invariant, the normalized empirical distribution process converges in distribution to a centered…
In this paper we consider a branching particle system consisting of particles moving according to the Ornstein-Uhlenbeck process in $\Rd$ and undergoing a binary, supercritical branching with a constant rate $\lambda>0$. This system is…
We study the motion of an overdamped colloidal particle in a time-dependent non-harmonic potential. We demonstrate the first law-like balance between applied work, exchanged heat, and internal energy on the level of a single trajectory. The…
In this paper, we present a fluctuation analysis of a type of parabolic equations with large, highly oscillatory, random potentials around the homogenization limit. With a Feynman-Kac representation, the Kipnis-Varadhan's method, and a…
Self-avoiding walks are studied on the 3-simplex fractal lattice as a model of linear polymer conformations in a dilute, non-homogeneous solution. A model is supplemented with bending energies and attractive-interaction energies between…
We provide new limit theory for functionals of a general class of processes lying at the boundary between stationarity and nonstationarity -- what we term weakly nonstationary processes (WNPs). This includes, as leading examples, fractional…
We study the transport properties of disordered two-dimensional electron systems with a perfectly conducting channel. We introduce an asymmetric Chalker-Coddington network model and numerically investigate the point-contact conductance. We…