2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/61369We introduce a new method for studying large scale properties of random walks. The new concepts of transience and recurrence on the average are compared with the ones introduced by R.Burioni, D.Cassi and A.Vezzani and with the usual ones; their relationships are analyzed and various examples are provided.Reduced number of pages to 28, added final paragraph of conclusions with some new resultsProbabilityFunctional Analysis82B41; 60G50text