Related papers: Non-equilibrium scaling limit for a tagged particl…
We prove the law of large numbers and invariance principles for the tagged particle in the asymmetric exclusion process with long jumps when the process starts from its equilibrium measure.
We prove a law of large numbers and a central limit theorem for a tagged particle in a symmetric simple exclusion process in the one-dimensional lattice with variable diffusion coefficient. The scaling limits are obtained from a similar…
We consider some interacting particle processes with long-range dynamics: the zero-range and exclusion processes with long jumps. We prove that the hydrodynamic limit of these processes corresponds to a (possibly non-linear) fractional heat…
We prove a nonequilibirum central limit theorem for the position of a tagged particle in the one-dimensional nearest-neighbor symmetric simple exclusion process under diffusive scaling starting from a Bernoulli product measure associated to…
For a sequence of i.i.d. random variables $\{\xi_x : x\in \bb Z\}$ bounded above and below by strictly positive finite constants, consider the nearest-neighbor one-dimensional simple exclusion process in which a particle at $x$ (resp.…
We consider the asymmetric exclusion process with a driven tagged particle on Z which has different jump rates from other particles and show that the tagged particle can have a ballistic behavior when the non-tagged particles have…
We study the equilibrium fluctuations of a tagged particle in finite-range simple exclusion processes on Z^d with biased single particle jump rates. It is known the variance of the tagged particle at time t is diffusive, that is on order…
We prove a non-equilibrium functional central limit theorem for the position of a tagged particle in mean-zero one-dimensional zero-range process. The asymptotic behavior of the tagged particle is described by a stochastic differential…
We determine analytically the dependence of the approach to thermal equilibrium of strongly coupled plasmas on the breaking of scale invariance. The theories we consider are the holographic duals to Einstein gravity coupled to a scalar with…
We consider a driven tagged particle in a symmetric exclusion process on Z with a removal rule. In this process, untagged particles are removed once they jump to the left of the tagged particle. We investigate the behavior of the…
We consider the stochastic ranking process with space-time dependent jump rates for the particles. The process is a simplified model of the time evolution of the rankings such as sales ranks at online bookstores. We prove that the joint…
The scaling invariance for chaotic orbits near a transition from unlimited to limited diffusion in a dissipative standard mapping is explained via the analytical solution of the diffusion equation. It gives the probability of observing a…
We give a derivation of tagged particle processes from unlabeled interacting Brownian motions. We give a criteria of the non-explosion property of tagged particle processes. We prove the quasi-regularity of Dirichlet forms describing the…
We prove a weak law of large numbers for a tagged particle in a totally asymmetric exclusion process on the one-dimensional lattice. The particles are allowed to take long jumps but not pass each other. The object of the paper is to…
We establish an invariance principle for a one-dimensional random walk in a dynamical random environment given by a speed-change exclusion process. The jump probabilities of the walk depend on the configuration of the exclusion in a finite…
This paper is devoted to establish an invariance principle where the limit process is a multifractional Gaussian process with a multifractional function which takes its values in $(1/2,1)$. Some properties, such as regularity and local…
The exclusion process in which particles may jump any distance l>=1 with the probability that decays as l^-(1+sigma) is studied from coarse-grained equation for density profile in the limit when the lattice spacing goes to zero. For…
We consider the limit behavior of a one-dimensional random walk with unit jumps whose transition probabilities are modified every time the walk hits zero. The invariance principle is proved in the scheme of series where the size of…
We discuss the scaling of the interaction energy with particle numbers for a harmonically trapped two-species mixture at thermal equilibrium experiencing interactions of arbitrary strength and range. In the limit of long-range interactions…
We study finite particle systems on the one-dimensional integer lattice, where each particle performs a continuous-time nearest-neighbour random walk, with jump rates intrinsic to each particle, subject to an exclusion interaction which…