An equivalence of \(H_{-1}\) norms for the simple exclusion process
type: Item
instance of: scholarly article
title: An equivalence of \(H_{-1}\) norms for the simple exclusion process
zbMATH Open document ID: 1019.60091
author: Sunder Sethuraman
published in: The Annals of Probability
publication date: 2003-05-06T00:00:00Z
review text: Resolvent \(H_{-1}\) norms with respect to simple exclusion processes play an important role in many problems with respect to additive functionals, tagged particles, hydrodynamics and so on. The author extends the norms to general (asymmetric) translation-invariant finite-range simple exclusion processes. As usual, the asymmetry costs a lot of problems. Based on a recent result by S. R. S. Varadhan, for the standard system of indistinguishable particles, the author proves that the corresponding resolvent \(H_{-1}\) norms are equivalent, in a sense, to the \(H_{-1}\) norms of a nearest-neighbor system. The same assertion is proved for systems with a distinguished particle in dimensions \(d\geq 2\), and 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.
Mathematics Subject Classification ID: 60K35
zbMATH DE Number: 1906114
zbMATH Keywords: exclusion process
zbMATH Keywords: hydrodynamics
zbMATH Keywords: resolvent norm
reviewed by: Mu-Fa Chen
MaRDI profile type: Publication
full work available at URL: https://doi.org/10.1214/aop/1046294303
OpenAlex ID: W2091165765
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DOI: 10.1214/AOP/1046294303
description: scientific article; zbMATH DE number 1906114