We consider random walks in a random environment which are generalized versions of well-known effective models for Mott variablerange hopping. We study the homogenized diffusion constant of the random walk in the one-dimensional case. We prove various estimates on the low-temperature behavior which confirm and extend previous work by physicists. 1. Introduction. Random

Abstract. We consider reversible random walks in random environment obtained from symmetric long–range jump rates on a random point process. We prove almost sure transience and recurrence results under suitable assumptions on the point process and the jump rate function. For recurrent models we obtain almost sure estimates on effective resistances in finite boxes. For transient models we construct explicit fluxes with finite energy on the associated electrical network. Key words: random walk in random environment, recurrence, transience, point process,