Central limit theorems for additive functionals of the simple exclusion process

By S. Sethuraman. 2006

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Definition 2.1 in the above paper is incorrectly stated. In the proof of Theo rem 2.1, which gives an invariance principle for certain processes satisfying Defi nition 2.1, conditions in Definition 2.1 are sufficient to deduce finite-dimensional convergence, but not enough to apply a maximal inequality for "demimartingales" to obtain tightness. The problem is Definition 2.1, as stated, only considers "pair increment associations" and not more general associations needed for the demi martingale property. We slightly strengthen the definition here in this correction so that the proof of tightness in Theorem 2.1 holds. Details of how this is accom plished are given below. By substituting the corrected Definition 2.1 for the previous one, all results in the article hold as written. In particular, Proposition 2.1, which is the link between Theorem 2.1 and the main results, and which states certain additive processes sat isfy Definition 2.1, holds with the same argument.

Subfields: Management Science and Operations Research, Mathematical Physics, Statistics and Probability

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