Abstract
We prove a central limit theorem under diffusive scaling for the displacement of a random walk on Ζ^{d} in stationary and ergodic doubly stochastic random environment, under the Η_{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 [10], 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 [8], and is technically rather simpler than existing earlier proofs of similar results by Oelschläger [19] and Komorowski, Landim and Olla [10].
Original language  English 

Pages (fromto)  43074347 
Number of pages  41 
Journal  Annals of Probability 
Volume  45 
Issue number  6B 
DOIs  
Publication status  Published  12 Dec 2017 
Keywords
 random walk in random environment
 central limit theorem
 KipnisVaradhan theory
 sector condition
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Professor Balint A Toth
 School of Mathematics  Chair in Probability
 Probability, Analysis and Dynamics
 Probability
Person: Academic , Member, Group lead