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

• 成果类型: Article
• 署名作者: Sethuraman, S
• 署名单位: Iowa State University
• 刊物名称: ANNALS OF PROBABILITY
• ISSN/ISSBN: 0091-1798
• 发表日期: 2003
• 页码: 35-62
• 关键词: CENTRAL LIMIT-THEOREMS; tagged particle; additive-functionals; systems

摘要

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 greater than or equal to 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.