### Abstract

Resolvent H_{-1} norms with respect to simple exclusion processes play an important role in many problems with respect to additive functionals, tagged particles, and hydrodynamics, among other concerns. Here, general translation-invariant finite-range simple exclusion processes with and without a distinguished particle are considered. For the standard system of indistinguishable particles, it is proved that the corresponding H_{-1} norms are equivalent, in a sense, to the H_{-1} norms of a nearest-neighbor system. The same result holds for systems with a distinguished particle in dimensions d ≥ 2. However, in dimension d = 1, this equivalence does not hold. An application of the H_{-1} norm equivalence to additive functional variances is also given.

Original language | English (US) |
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Pages (from-to) | 35-62 |

Number of pages | 28 |

Journal | Annals of Probability |

Volume | 31 |

Issue number | 1 |

DOIs | |

State | Published - Jan 2003 |

Externally published | Yes |

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### Keywords

- Simple exclusion process H
- Variance norms

### ASJC Scopus subject areas

- Mathematics(all)
- Statistics and Probability

### Cite this

**An equivalence of H _{-1} norms for the simple exclusion process.** / Sethuraman, Sunder.

Research output: Contribution to journal › Article

_{-1}norms for the simple exclusion process',

*Annals of Probability*, vol. 31, no. 1, pp. 35-62. https://doi.org/10.1214/aop/1046294303

}

TY - JOUR

T1 - An equivalence of H-1 norms for the simple exclusion process

AU - Sethuraman, Sunder

PY - 2003/1

Y1 - 2003/1

N2 - Resolvent H-1 norms with respect to simple exclusion processes play an important role in many problems with respect to additive functionals, tagged particles, and hydrodynamics, among other concerns. Here, general translation-invariant finite-range simple exclusion processes with and without a distinguished particle are considered. For the standard system of indistinguishable particles, it is proved that the corresponding H-1 norms are equivalent, in a sense, to the H-1 norms of a nearest-neighbor system. The same result holds for systems with a distinguished particle in dimensions d ≥ 2. However, in dimension d = 1, this equivalence does not hold. An application of the H-1 norm equivalence to additive functional variances is also given.

AB - Resolvent H-1 norms with respect to simple exclusion processes play an important role in many problems with respect to additive functionals, tagged particles, and hydrodynamics, among other concerns. Here, general translation-invariant finite-range simple exclusion processes with and without a distinguished particle are considered. For the standard system of indistinguishable particles, it is proved that the corresponding H-1 norms are equivalent, in a sense, to the H-1 norms of a nearest-neighbor system. The same result holds for systems with a distinguished particle in dimensions d ≥ 2. However, in dimension d = 1, this equivalence does not hold. An application of the H-1 norm equivalence to additive functional variances is also given.

KW - Simple exclusion process H

KW - Variance norms

UR - http://www.scopus.com/inward/record.url?scp=0037251442&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=0037251442&partnerID=8YFLogxK

U2 - 10.1214/aop/1046294303

DO - 10.1214/aop/1046294303

M3 - Article

VL - 31

SP - 35

EP - 62

JO - Annals of Probability

JF - Annals of Probability

SN - 0091-1798

IS - 1

ER -