Abstract
We consider an i.i.d. random environment with a strong form of transience on the two dimensional integer lattice. Namely, the walk always moves forward in the y-direction. We prove an invariance principle for the quenched expected position of the random walk indexed by its level crossing times. We begin with a variation of the Martingale Central Limit Theorem. The main part of the paper checks the conditions of the theorem for our problem.
Citation
Mathew Joseph. "Fluctuations of the quenched mean of a planar random walk in an i.i.d. random environment with forbidden direction." Electron. J. Probab. 14 1268 - 1289, 2009. https://doi.org/10.1214/EJP.v14-655
Information