Central Limit Theorem for Random Walks in Doubly Stochastic Random Environment: H_-1 Suffices

2017/02/22 by Kozma, Gady, Tóth, Bálint
#60F05 #60G99 #60K37 #FOS: Mathematics #Probability (math.PR)

paper · doi:10.48550/arxiv.1702.06905

Abstract

We prove a central limit theorem under diffusive scaling for the displacement of a random walk on \mathbb Z^d in stationary and ergodic doubly stochastic random environment, under the H_-1-condition imposed on the drift field. The condition is equivalent to assuming that the stream tensor of the drift field be stationary and square integrable. This improves the best existing result of Komorowski, Landim and Olla (2012), where it is assumed that the stream tensor is in L^max\2+δ, d\, with δ>0. Our proof relies on an extension of the relaxed sector condition of Horváth, Tóth and Vető (2012) and is technically rather simpler than existing earlier proofs of similar results by Oelschläger (1988) and Komorowski, Landim and Olla (2012)

Related

• Central limit theorem for random walks in divergence-free random drift field: "H-minus-one" suffices
• Quenched Central Limit Theorem for Random Walks in Doubly Stochastic\n Random Environment
• Almost sure functional central limit theorem for non-nestling random walk in random environment
• The quenched central limit theorem for a model of random walk in random\n environment
• Simple Transient Random Walks in One-dimensional Random Environment: the Central Limit Theorem