Related papers: Superdiffusivity of asymmetric exclusion process i…
We analyze upwind difference methods for strongly degenerate convection-diffusion equations in several spatial dimensions. We prove that the local $L^1$-error between the exact and numerical solutions is $\mathcal{O}(\Delta x^{2/(19+d)})$,…
By using the spectrum of the underlying symmetric diffusion operator, the convergence in $L^p$-Wasserstein distance $\mathbb W_p (p\ge 1)$ is characterized for the empirical measure $\mu_t$ of non-symmetric subordinated diffusion processes…
The effect of a moving defect particle for the one-dimensional partially asymmetric simple exclusion process on a ring is considered. The current of the ordinary particles, the speed of the defect particle and the density profile of the…
The paper presents new simple sharp bounds for transition density functions for time-homogeneous diffusions processes. The bounds are obtained under mild conditions on the drift and diffusion coefficients, extending and substantially…
We prove a nonstandard central limit theorem and weak invariance principle, with superdiffusive normalisation $(t\log t)^{1/2}$, for geodesic flows on a class of nonpositively curved surfaces with flat cylinder. We also prove that…
In this paper, we address a time-dependent one-dimensional linear advection-diffusion equation with Dirichlet homogeneous boundary conditions. The equation is solved both analytically, using separation of variables, and numerically,…
We provide a both qualitative and quantitative comparison among different approaches aimed to solve the problem of non-linear diffusive acceleration of particles at shocks. In particular, we show that state-of-the-art models (numerical,…
We consider the Halfin-Whitt diffusion process $X_d(t)$, which is used, for example, as an approximation to the $m$-server $M/M/m$ queue. We use recently obtained integral representations for the transient density $p(x,t)$ of this diffusion…
We consider single-file diffusion in an open system with two species $A,B$ of particles. At the boundaries we assume different reservoir densities which drive the system into a non-equilibrium steady state. As a model we use an…
We prove that the variance of the current across a characteristic is of order t^{2/3} in a stationary constant rate totally asymmetric zero range process, and that the diffusivity has order t^{1/3}. This is a step towards proving…
The prediction of diffusion in solids is necessary to understand the microstructure evolution in materials out of equilibrium. Although one can reasonably predict diffusive transport coefficients using atomistic methods, these approaches…
We study the diffusion-limited process $A+A\to A$ in one dimension, with finite reaction rates. We develop an approximation scheme based on the method of Inter-Particle Distribution Functions (IPDF), which was formerly used for the exact…
Consider a system of particles performing nearest neighbor random walks on the lattice $\ZZ$ under hard--core interaction. The rate for a jump over a given bond is direction--independent and the inverse of the jump rates are i.i.d. random…
We develop several statistical tests of the determinant of the diffusion coefficient of a stochastic differential equation, based on discrete observations on a time interval $[0,T]$ sampled with a time step $\Delta$. Our main contribution…
We extend one dimensional asymmetric simple exclusion process (ASEP) to a surface and show that the effect of transverse diffusion is to induce a continuous phase transition from a constant density phase to a maximal current phase as the…
An integrable asymmetric exclusion process with impurities is formulated. The model displays the full spectrum of the stochastic asymmetric XXZ chain plus new levels. We derive the Bethe equations and calculate the spectral gap for the…
We consider two Ito equations that evolve on different time scales. The equations are fully coupled in the sense that all coefficients may depend on both the "slow" and the "fast" processes and the diffusion terms may be correlated. The…
We study a symmetric randomly moving line interacting by exclusion with a wall. We show that the expectation of the position of the line at the origin when it starts attached to the wall satisfies the following bounds: c_1t^{1/4}…
The aim of this paper is to study the behavior of the weighted empirical measures of the decreasing step Euler scheme of a one-dimensional diffusion process having multiple invariant measures. This situation can occur when the drift and the…
Differentiability of semigroups is useful for many applications. Here we focus on stochastic differential equations whose diffusion coefficient is the square root of a differentiable function but not differentiable itself. For every…