Abstract
We prove a functional central limit theorem for additive functionals of stationary reversible ergodic Markov chains under virtually no assumptions other than the necessary ones. We use these results to study the asymptotic behavior of a tagged particle in an infinite particle system performing simple excluded random walk.
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Communicated by J. L. Lebowitz
Supported by NSF Grant MCS-8301364, ONR Contract N00014-81-K-0012 and a Fellowship from John S. Guggenheim Memorial Foundation
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Kipnis, C., Varadhan, S.R.S. Central limit theorem for additive functionals of reversible Markov processes and applications to simple exclusions. Commun.Math. Phys. 104, 1–19 (1986). https://doi.org/10.1007/BF01210789
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DOI: https://doi.org/10.1007/BF01210789