Random walks in quenched i.i.d. space-time random environment are always a.s. diffusive

• Published in: Probability theory and related fields Vol. 129; no. 1; pp. 133 - 156
• Main Authors: Boldrighini, C, Minlos, R A, Pellegrinotti, A
• Format: Journal Article
• Language: English
• Published: Heidelberg Springer Nature B.V 01.05.2004
• Subjects: Central limit theorem; Mathematics; Norms; Probability; Quenching; Random variables; Random walk; Spacetime; Theorems

We consider a general model of discrete-time random walk Xt on the lattice ν, ν = 1,..., in a random environment ξ={ξ(t,x):(t,x)∈ν+1} with i.i.d. components ξ(t,x). Previous results on the a.s. validity of the Central Limit Theorem for the quenched model required a small stochasticity condition. In...