相关论文: Disordered exclusion process revisited: some exact…
We obtain the exact large deviation functions of the density profile and of the current, in the non-equilibrium steady state of a one dimensional symmetric simple exclusion process coupled to boundary reservoirs with slow rates. Compared to…
Consider the open symmetric exclusion process on a connected graph with vertexes in $[N-1]:=\{1,\ldots, N-1\}$ where points $1$ and $N-1$ are connected, respectively, to a left reservoir and a right reservoir with densities…
Characterizing current fluctuations in a steady state is of fundamental interest and has attracted considerable attention in the recent past. However, the bulk of the studies are limited to systems that either do not exhibit a phase…
In this paper, we study an exact solution of the asymmetric simple exclusion process on a periodic lattice of finite sites with two typical updates, i.e., random and parallel. Then, we find that the explicit formulas for the partition…
As a solvable and broadly applicable model system, the totally asymmetric exclusion process enjoys iconic status in the theory of non-equilibrium phase transitions. Here, we focus on the time dependence of the total number of particles on a…
We consider the asymmetric simple exclusion process on a ring, with an arbitrary asymmetry between the hopping rates of the particles. Using a functional formulation of the Bethe equations of the model, we derive exact expressions for all…
In the recent past, there has been a concerted effort to develop mathematical models for real-world networks and to analyze various dynamics on these models. One particular problem of significant importance is to understand the effect of…
We study analytically the effect of a correlated random potential on the persistent current in a one-dimensional ring threaded by a magnetic flux $\phi$, using an Anderson tight-binding model. In our model, the system of $N=2M$ atomic sites…
We analyze the equilibrium fluctuations of the density, current and tagged particle in symmetric exclusion with a slow bond. The system evolves in the one-dimensional lattice and the jump rate is everywhere equal to one except at the slow…
We consider random walks on marked simple point processes with symmetric jump rates and unbounded jump range. We prove homogenization properties of the associated Markov generators. As an application, we derive the hydrodynamic limit of the…
We study large deviations for the current of one-dimensional stochastic particle systems with periodic boundary conditions. Following a recent approach based on an earlier result by Jensen and Varadhan, we compare several candidates for…
We study the one-dimensional asymmetric simple exclusion process on the lattice $\{1, \dots,N\}$ with creation/annihilation at the boundaries. The boundary rates are time dependent and change on a slow time scale $N^{-a}$ with $a>0$. We…
This paper studies the quasi-stationary distributions for a single death process (or downwardly skip-free process) with killing defined on the non-negative integers, corresponding to a non-conservative transition rate matrix. The set…
We consider the problem of minimizing queue-length costs in a system with heterogenous parallel servers, operating in a many-server heavy-traffic regime with nondegenerate slowdown. This regime is distinct from the well-studied heavy…
Recurrent neural networks with balanced excitation and inhibition exhibit irregular asynchronous dynamics, which is fundamental for cortical computations. Classical balance mechanisms require strong external inputs to sustain finite firing…
We explore the possibility of obtaining unidirectional current in a symmetric (periodic) potential system without the application of any obvious (apparent) externally applied bias. There are many physical models proposed to accomplish this…
We study an open system composed of two parallel totally asymmetric simple exclusion processes with particle attachment and detachment in the bulk. The particles are allowed to change their lane from lane-A to lane-B, but not conversely. We…
We provide a full description for the joint fluctuations of current and occupation time in the one-dimensional nonequilibrium simple symmetric exclusion process, furnishing explicit formulas for the covariances of the limiting Gaussian…
We perform network analysis of a system described by the master equation to estimate the lower bound of the steady-state current noise, starting from the level 2.5 large deviation function and using the graph theory approach. When the…
We consider an Asymmetric Exclusion Process evolving on parallel mutually interacting lanes with neighbouring nearest hoppings of hardcore particles. Number of particles on each lane is conserved. We find a choice of the hopping rates, for…