### Abstract

We give easily verifiable conditions under which a functional central limit theorem holds for additive functionals of symmetric simple exclusion and symmetric zero-range processes. Also a reversible exclusion model with speed change is considered. Let η(t) be the configuration of the process at time t and let f(η) be a function on the state space. The question is: For which functions f does λ ^{-1/2}∫^{λt}_{0} f(η(s)) ds converge to a Brownian motion? A general but often intractable answer is given by Kipnis and Varadhan. In this article we determine what conditions beyond a mean-zero condition on f(η) are required for the diffusive limit above. Specifically, we characterize the H^{-1} space in an applicable way. Our method of proof relies primarily on a sharp estimate on the "spectral gap" of the process and weak regularity properties for the invariant measures.

Original language | English (US) |
---|---|

Pages (from-to) | 1842-1870 |

Number of pages | 29 |

Journal | Annals of Probability |

Volume | 24 |

Issue number | 4 |

State | Published - Oct 1996 |

Externally published | Yes |

### Fingerprint

### Keywords

- Central limit theorem
- Invariance principle
- Simple exclusion process
- Zero-range process

### ASJC Scopus subject areas

- Mathematics(all)
- Statistics and Probability

### Cite this

*Annals of Probability*,

*24*(4), 1842-1870.

**A central limit theorem for reversible exclusion and zero-range particle systems.** / Sethuraman, Sunder; Xu, Lin.

Research output: Contribution to journal › Article

*Annals of Probability*, vol. 24, no. 4, pp. 1842-1870.

}

TY - JOUR

T1 - A central limit theorem for reversible exclusion and zero-range particle systems

AU - Sethuraman, Sunder

AU - Xu, Lin

PY - 1996/10

Y1 - 1996/10

N2 - We give easily verifiable conditions under which a functional central limit theorem holds for additive functionals of symmetric simple exclusion and symmetric zero-range processes. Also a reversible exclusion model with speed change is considered. Let η(t) be the configuration of the process at time t and let f(η) be a function on the state space. The question is: For which functions f does λ -1/2∫λt0 f(η(s)) ds converge to a Brownian motion? A general but often intractable answer is given by Kipnis and Varadhan. In this article we determine what conditions beyond a mean-zero condition on f(η) are required for the diffusive limit above. Specifically, we characterize the H-1 space in an applicable way. Our method of proof relies primarily on a sharp estimate on the "spectral gap" of the process and weak regularity properties for the invariant measures.

AB - We give easily verifiable conditions under which a functional central limit theorem holds for additive functionals of symmetric simple exclusion and symmetric zero-range processes. Also a reversible exclusion model with speed change is considered. Let η(t) be the configuration of the process at time t and let f(η) be a function on the state space. The question is: For which functions f does λ -1/2∫λt0 f(η(s)) ds converge to a Brownian motion? A general but often intractable answer is given by Kipnis and Varadhan. In this article we determine what conditions beyond a mean-zero condition on f(η) are required for the diffusive limit above. Specifically, we characterize the H-1 space in an applicable way. Our method of proof relies primarily on a sharp estimate on the "spectral gap" of the process and weak regularity properties for the invariant measures.

KW - Central limit theorem

KW - Invariance principle

KW - Simple exclusion process

KW - Zero-range process

UR - http://www.scopus.com/inward/record.url?scp=0030356324&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=0030356324&partnerID=8YFLogxK

M3 - Article

VL - 24

SP - 1842

EP - 1870

JO - Annals of Probability

JF - Annals of Probability

SN - 0091-1798

IS - 4

ER -