Geodesic
Anomalous Behaviour of the Correction to the Central Limit Theorem for a Model of Random Walk in Random Media
Bollettino della Unione matematica italiana, Série 9, Tome 3 (2010) no. 1, pp. 179-206.

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We give a result concerning the correction to the Central Limit Theorem for a Random Walk on the lattice $\mathbf{Z}^{2}$ which interacts with a random environment under a small randomness condition. Our main theorem close a gap which dates back to seminal works by Boldrighini, Minlos and Pellegrinotti, see [3], [8] and [9]. Asymptotic behaviour of the corrections to the average and the covariance matrix in dimension $\nu = 1,2$ are also presented. 
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Di Persio, L. Anomalous Behaviour of the Correction to the Central Limit Theorem for a Model of Random Walk in Random Media. Bollettino della Unione matematica italiana, Série 9, Tome 3 (2010) no. 1, pp. 179-206. http://geodesic.mathdoc.fr/item/BUMI_2010_9_3_1_a8/

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