### Abstract

We review in this article central limit theorems for a tagged particle in the simple exclusion process. In the first two sections we present a general method to prove central limit theorems for additive functional of Markov processes. These results are then applied to the case of a tagged particle in the exclusion process. Related questions, such as smoothness of the diffusion coefficient and finite dimensional approximations, are considered in the last section.

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

Pages (from-to) | 241-275 |

Number of pages | 35 |

Journal | Bulletin of the Brazilian Mathematical Society |

Volume | 31 |

Issue number | 3 |

State | Published - 2000 |

### Fingerprint

### Keywords

- Central limit theorem
- Interacting particles systems
- Tagged particle

### ASJC Scopus subject areas

- Mathematics(all)

### Cite this

*Bulletin of the Brazilian Mathematical Society*,

*31*(3), 241-275.

**Asymptotic behavior of a tagged particle in simple exclusion processes.** / Landim, C.; Olla, S.; Varadhan, Srinivasa.

Research output: Contribution to journal › Article

*Bulletin of the Brazilian Mathematical Society*, vol. 31, no. 3, pp. 241-275.

}

TY - JOUR

T1 - Asymptotic behavior of a tagged particle in simple exclusion processes

AU - Landim, C.

AU - Olla, S.

AU - Varadhan, Srinivasa

PY - 2000

Y1 - 2000

N2 - We review in this article central limit theorems for a tagged particle in the simple exclusion process. In the first two sections we present a general method to prove central limit theorems for additive functional of Markov processes. These results are then applied to the case of a tagged particle in the exclusion process. Related questions, such as smoothness of the diffusion coefficient and finite dimensional approximations, are considered in the last section.

AB - We review in this article central limit theorems for a tagged particle in the simple exclusion process. In the first two sections we present a general method to prove central limit theorems for additive functional of Markov processes. These results are then applied to the case of a tagged particle in the exclusion process. Related questions, such as smoothness of the diffusion coefficient and finite dimensional approximations, are considered in the last section.

KW - Central limit theorem

KW - Interacting particles systems

KW - Tagged particle

UR - http://www.scopus.com/inward/record.url?scp=0013498819&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=0013498819&partnerID=8YFLogxK

M3 - Article

VL - 31

SP - 241

EP - 275

JO - Bulletin of the Brazilian Mathematical Society

JF - Bulletin of the Brazilian Mathematical Society

SN - 1678-7544

IS - 3

ER -