Related papers: Blocks and Gaps in the Asymmetric Simple Exclusion…
We consider the stationary measure of the open asymmetric simple exclusion process (ASEP) with light particles. We prove several results on the asymptotic locations of the light particles under the stationary measure. Moreover, in the fan…
We consider from a microscopic perspective large deviation properties of several stochastic interacting particle systems, using their mapping to integrable quantum spin systems. A brief review of recent work is given and several new results…
We study the asymptotic behaviour of the probability that a stochastic process $(Z_t)_{t \geq 0}$ does not exceed a constant barrier up to time $T$ (the so called survival probability) when Z is the composition of two independent processes…
The purpose of this article is to describe the two approaches to compute exact formulas (which are amenable to asymptotic analysis) for the probability distribution of the current of particles past a given site in the asymmetric simple…
We consider the periodic totally asymmetric simple exclusion process with a general initial condition that properly approximates a periodic upper-semicontinuous function. We find the large time limit of the rescaled space-time multipoint…
We consider the totally asymmetric simple exclusion process with initial conditions and/or jump rates such that shocks are generated. If the initial condition is deterministic, then the shock at time t will have a width of order t^{1/3}. We…
We propose an extension of the totally asymmetric simple exclusion process (TASEP) in which particles hopping along a lattice can be blocked by obstacles that dynamically attach/detach from lattice sites. The model can be thought as TASEP…
We prove sharp asymptotic estimates for the rate of escape of the two-dimensional simple random walk conditioned to avoid a fixed finite set. We derive it from asymptotics available for the continuous analogue of this process (cf…
In this paper we analyze the steady state of the Asymmetric Simple Exclusion process with open boundaries and second class particles by deforming it through the introduction of spectral parameters. The (unnormalized) probabilities of the…
We consider the asymmetric simple exclusion process (ASEP) with open boundary condition at the left boundary, where particles exit at rate {\gamma} and enter at rate {\alpha} = {\gamma}{\tau}^2, and where {\tau} is the asymmetry parameter…
We derive logarithmic asymptotics of probabilities of small deviations for iterated processes in the space of trajectories. We find conditions under which these asymptotics coincide with those of processes generating iterated processes.…
A traffic model on an open one-dimensional lattice is considered. At any discrete time moment, with prescribed probability, a particle arrives to the leftmost cell of the lattice, and, with prescribed probability, the arriving particle…
As the simplest model of transport of interacting particles in a disordered medium, we consider the asymmetric simple exclusion process (ASEP) in which particles with hard-core interactions perform biased random walks, on the supercritical…
We study a one-dimensional totally asymmetric simple exclusion process with one special site from which particles fly to any empty site (not just to the neighboring site). The system attains a non-trivial stationary state with density…
We consider the corner growth dynamics on discrete bridges from $(0,0)$ to $(2N,0)$, or equivalently, the weakly asymmetric simple exclusion process with $N$ particles on $2N$ sites. We take an asymmetry of order $N^{-\alpha}$ with $\alpha…
We introduce a class of facilitated asymmetric exclusion processes in which particles are pushed by neighbors from behind. For the simplest version in which a particle can hop to its vacant right neighbor only if its left neighbor is…
We consider the probability that no points lie on $g$ large intervals in the bulk of the Airy point process. We make a conjecture for all the terms in the asymptotics up to and including the oscillations of order $1$, and we prove this…
The singular values of a product of $M$ independent Ginibre matrices of size $N\times N$ form a determinantal point process. Near the soft edge, as both $M$ and $N$ go to infinity in such a way that $M/N\to \alpha$, $\alpha>0$, a scaling…
We consider the behavior of extremal particles in $K$-symmetric exclusion on $\mathbb{Z}$ when the process starts from certain infinite-particle step configurations where there are no particles to the right of a maximal one. In such a…
We consider a version of random motion of hard core particles on the semi-lattice $ 1, 2, 3,...$, where in each time instant one of three possible events occurs, viz., (a) a randomly chosen particle hops to a free neighboring site, (b) a…