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We prove the quenched version of the central limit theorem for thedisplacement of a random walk in doubly stochastic random environment, underthe $H_{-1}$-condition, with slightly stronger, $L^{2+\varepsilon}$ (ratherthan $L^2$) integrability condition on the stream tensor. On the way we extendNash's moment bound to the non-reversible, divergence-free drift case.

Quenched Central Limit Theorem for Random Walks in Doubly Stochastic Random Environment