Inhomogeneous long-range percolation in the strong decay regime: recurrence in one dimension

Abstract

We provide a sufficient criterion for the recurrence of spatial random graphs on the real line based on the scarceness of long-edges. In particular, this complements earlier recurrence results obtained by Gracar et al. (Electron. J. Probab. 27 (2022)) and a transience criterion derived by the author (Probab. Theory Related Fields 189, no. 3-4 (2024)).

v2: manuscript unchanged; the present preprint is superseded by arXiv:2608.25201 which extends the results to include dimension 2