Related papers: Limiting current distribution for a two species as…
We study a system of drift-diffusion PDEs for a potentially infinite number of incompressible phases, subject to a joint pointwise volume constraint. Our analysis is based on the interpretation as a collection of coupled Wasserstein…
We derive a universal bound on the large-deviation functions of particle currents in coherent conductors. This bound depends only on the mean value of the relevant current and the total rate of entropy production required to maintain a…
We compare two approaches to nonequilibrium thermodynamics, the two-generator bracket formulation of time-evolution equations for averages and the macroscopic fluctuation theory, for an isothermal driven diffusive system under steady state…
We work towards the classification of all one-dimensional exclusion processes with two species of particles that can be solved by a nested coordinate Bethe Ansatz. Using the Yang-Baxter equations, we obtain conditions on the model…
The one-dimensional totally asymmetric simple exclusion process (TASEP) is considered. We study the time evolution property of a tagged particle in TASEP with the step-type initial condition. Calculated is the multi-time joint distribution…
We provide an estimation of the dissipation of the Wasserstein 2 distance between the law of some interacting $N$-particle system, and the $N$ times tensorized product of solution to the corresponding limit nonlinear conservation law. It…
We present a general framework to study the distribution of the flux through the origin up to time $t$, in a non-interacting one-dimensional system of particles with a step initial condition with a fixed density $\rho$ of particles to the…
We study lower large deviations for the current of totally asymmetric zero-range processes on a ring with concave current-density relation. We use an approach by Jensen and Varadhan which has previously been applied to exclusion processes,…
This paper is the continuation of our earlier paper, where we proved t^{1/3}-order of current fluctuations across the characteristics in a class of one dimensional interacting systems with one conserved quantity. We also claimed two models…
Suppose $X$ is a multidimensional diffusion process. Assume that at time zero the state of $X$ is fully observed, but at time $T>0$ only linear combinations of its components are observed. That is, one only observes the vector $L X_T$ for a…
By using the coupling technique, we present sufficient conditions for the exponential ergodicity of general continuous-state nonlinear branching processes in both the $L^1$-Wasserstein distance and the total variation norm, where the drift…
The presented explanations are provided for the one--dimensional diffusion process with constant drift by using forward Fokker--Planck technique. We are interested in the outflow probability in a finite interval, i.e. first passage time…
In this paper we consider inhomogeneous Galton-Watson trees, and derive various moments for such processes: the number of vertices, the number of leaves, and the height of the tree. Also we make a simple condition of finiteness. We use…
A class of exclusion processes in which particles perform history-dependent random walks is introduced, stimulated by dynamic phenomena in some biological and artificial systems. The particles locally interact with the underlying substrate…
A new class of models, generalizing Asymmetric Exclusion Process for many parallel interacting channels, is proposed. We couple the models with boundary reservoirs, study boundary-driven phase transitions and show that usually taken…
The violation of the Pauli principle has been surmised in several models of the Fractional Exclusion Statistics and successfully applied to several quantum systems. In this paper, a classical alternative of the exclusion statistics is…
We study the large deviation functional of the current for the Weakly Asymmetric Simple Exclusion Process in contact with two reservoirs.We compare this functional in the large drift limit to the one of the Totally Asymmetric Simple…
Dunkl processes are generalizations of Brownian motion obtained by using the differential-difference operators known as Dunkl operators as a replacement of spatial partial derivatives in the heat equation. Special cases of these processes…
Probability currents are fundamental in characterizing the kinetics of non-equilibrium processes. Notably, the steady-state current $J_{ss}$ for a source-sink system can provide the exact mean-first-passage time (MFPT) for the transition…
We consider continuous-time random walks on a random locally finite subset of $\mathbb{R}^d$ with random symmetric jump probability rates. The jump range can be unbounded. We assume some second--moment conditions and that the above…