A limit theorem for quadratic fluctuations in symmetric simple exclusion

Jara

2013

Comm Pure Appl Math

ABSTRACT. Using the renormalization method introduced in [17], we prove what we call the local Boltzmann-Gibbs principle for conservative, stationary interacting particle systems in dimension d = 1. As applications of this result, we obtain various scaling limits of additive functionals of particle systems, like the occupation time of a given site or extensive additive fields of the dynamics. As a by-product of these results, we also construct a novel process, related to the stationary solution of the stochastic Burgers equation.

“…This theorem was first proved in [2]. In Section 5.3 we will present a different proof of this theorem, based on the so-called energy condition introduced in [17].…”

Section: Theorem 22 There Exists a Processmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

Scaling Limits of Additive Functionals of Interacting Particle Systems

Jara

2013

Comm Pure Appl Math

“…Notice that v t N + Z N t is a positive random variable since it corresponds to the number of holes in the interval [1 …”

Section: Dependence On the Initial Configurationmentioning

confidence: 99%

“…We start by showing condition (1). For each integer z ≥ 0, recall that h z denotes the Hermite function defined at the beginning of the …”

Section: Tightnessmentioning

confidence: 99%

Central limit theorem for a tagged particle in asymmetric simple exclusion

Stochastic Processes and their Applications

2008

We prove a functional central limit theorem for the position of a tagged particle in the one-dimensional asymmetric simple exclusion process for hyperbolic scaling, starting from a Bernoulli product measure conditioned to have a particle at the origin. We also prove that the position of the tagged particle at time t depends on the initial configuration, through the number of empty sites in the interval [0, ( p −q)αt] divided by α, on the hyperbolic time scale and on a longer time scale, namely N 4/3 .

Equilibrium Fluctuations for the Totally Asymmetric Zero-Range Process

2009

J Stat Phys

Abstract. We prove a Central Limit Theorem for the empirical measure in the one-dimensional Totally Asymmetric Zero-Range Process in the hyperbolic scaling N , starting from the equilibrium measure νρ. We also show that when taking the direction of the characteristics, the limit density fluctuation field does not evolve in time until N 4/3 , which implies the current across the characteristics to vanish in this longer time scale.