Oriented bond-site percolation in random environment and contact processes with periodic recovery

TL;DR

This paper studies percolation and contact processes on a lattice with stretched columns, establishing conditions for percolation and survival in environments with periodic or random recovery patterns.

Contribution

It generalizes recent results to include environments with stretched columns and proves survival of contact processes under these conditions.

Findings

Percolation occurs under a (1+ε)-moment condition on stretches.

Contact processes survive in environments with periodic recoveries.

Results extend to random environments with stretched columns.

Abstract

We investigate oriented bond-site percolation on the planar lattice in which entire columns are stretched. Generalising recent results by Hil\'ario et al., we establish non-trivial percolation under a $(1+\varepsilon)$-th moment condition on the stretches and use this to prove survival of contact processes with periodic recoveries as well as in random environments.