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January 2003 An equivalence of $H_{-1}$ norms for the simple exclusion process
Sunder Sethuraman
Ann. Probab. 31(1): 35-62 (January 2003). DOI: 10.1214/aop/1046294303

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 $d\geq 2$. 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.

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Sunder Sethuraman. "An equivalence of $H_{-1}$ norms for the simple exclusion process." Ann. Probab. 31 (1) 35 - 62, January 2003. https://doi.org/10.1214/aop/1046294303

Information

Published: January 2003
First available in Project Euclid: 26 February 2003

zbMATH: 1019.60091
MathSciNet: MR1959785
Digital Object Identifier: 10.1214/aop/1046294303

Subjects:
Primary: 60K35
Secondary: ‎46E99

Keywords: Simple exclusion process $H_{-1}$ , variance norms

Rights: Copyright © 2003 Institute of Mathematical Statistics

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Vol.31 • No. 1 • January 2003
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