Fluctuations of the quenched mean of a planar random walk in an i.i.d. Random environment with forbidden direction. (English) Zbl 1195.60130

Joseph, Mathew

Electron. J. Probab. 14, 1268-1289 (2009).

Summary: 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.

MSC:

60K37	Processes in random environments
60F05	Central limit and other weak theorems
60F17	Functional limit theorems; invariance principles
82B41	Random walks, random surfaces, lattice animals, etc. in equilibrium statistical mechanics
82B43	Percolation

Keywords:

random walk in random environment; central limit theorem; invariance principle; Green function