Central Limit Theorem and recurrence for random walks in bistochastic random environments

Abstract

We prove the annealed Central Limit Theorem for random walks in bistochastic random environments on $Z^d$ with zero local drift. The proof is based on a "dynamicist's interpretation" of the system, and requires a much weaker condition than the customary uniform ellipticity. Moreover, recurrence is derived for $d\le 2$.

13 pages; to appear in the special issue of J. Math. Phys. on "Statistical Mechanics on Random Structures"

References in corpus (5)

• Quenched invariance principle for simple random walk on percolation clusters
• Transience, Recurrence and Critical Behavior for Long-Range Percolation
• Typicality of recurrence for Lorentz gases
• Recurrence for persistent random walks in two dimensions
• Invariance Principle and recurrence for random walks in random environments with zero local drift

Cited by in corpus (5)

• Random walks in a one-dimensional Lévy random environment
• Recurrence for quenched random Lorentz tubes
• Uniformly expanding Markov maps of the real line: exactness and infinite mixing
• Random walks in random environments without ellipticity
• Recurrence and higher ergodic properties for quenched random Lorentz tubes in dimension bigger than two