Diffusive limit of a tagged particle in asymmetric simple exclusion processes

By S. Sethuraman, S. Varadhan, Horng-Tzer Yau. 2000

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Central limit theorems for additive functionals of the simple exclusion process (2006, unknown): “Informally, the question investigated is for which f does t−1/2 ∫ t 0 f η s ds converge weakly to a normal distribution N 0 σ2 f where η t is the configuration at time t? In this article, we examine this question with new ideas for finite-range exclusion processes with nonzero drift in all dimension”
Recent progress on the Random Conductance Model (2011, background): “Concerning departures from reversible situations, two lines of thought are generally being followed: One approach, drawing on the functionalanalytic ideas, goes by imposing (and checking) various sector conditions (e.g., Olla [110], Sethuraman, Varadhan and Yau [121], Horváth, Tóth and Vető [80])”