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We consider a recurrent RWRE $(X_n)_{n \in \mathbb{N}_0}$ on $\mathbb{Z}$ andinvestigate the quenched return probabilities of the RWRE to the origin forwhich we state results on their decay in terms of summability. Additionally, wegive some examples for recurrent RWRE with a multidimensional state space whichgive reason for the part "strong recurrence" in the title of this paper when wecompare the behaviour of RWRE with the behaviour of the symmetric random walkon $\mathbb{Z}^d$.

On the Strong Recurrence of Recurrent RWRE