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We consider a non-nestling random walk in a product random environment. Weassume an exponential moment for the step of the walk, uniformly in theenvironment. We prove an invariance principle (functional central limittheorem) under almost every environment for the centered and diffusively scaledwalk. The main point behind the invariance principle is that the quenched meanof the walk behaves subdiffusively.

Almost sure functional central limit theorem for non-nestling random walk in random environment