We consider a general model of discrete-time random walk X-t on the lattice (nu), nu = 1,..., in a random environment xi={xi(t,x):(t,x)is an element of(nu+1)} with i.i.d. components xi(t,x). Previous results on the a.s. validity of the Central Limit Theorem for the quenched model required a small stochasticity condition. In this paper we show that the result holds provided only that an obvious non-degeneracy condition is met. The proof is based on the analysis of a suitable generating function, which allows to estimate L-2 norms by contour integrals.
Random walks in quenched i.i.d. space-time random environment are always a.s. diffusive / Boldrighini, Carlo; R. A., Minlos; A., Pellegrinotti. - In: PROBABILITY THEORY AND RELATED FIELDS. - ISSN 0178-8051. - STAMPA. - 129:1(2004), pp. 133-156. [10.1007/s00440-003-0331-x]
Random walks in quenched i.i.d. space-time random environment are always a.s. diffusive
BOLDRIGHINI, Carlo;
2004
Abstract
We consider a general model of discrete-time random walk X-t on the lattice (nu), nu = 1,..., in a random environment xi={xi(t,x):(t,x)is an element of(nu+1)} with i.i.d. components xi(t,x). Previous results on the a.s. validity of the Central Limit Theorem for the quenched model required a small stochasticity condition. In this paper we show that the result holds provided only that an obvious non-degeneracy condition is met. The proof is based on the analysis of a suitable generating function, which allows to estimate L-2 norms by contour integrals.I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.
