For oriented bond-site percolation with columnar stretches, a (1+ε)-moment condition on stretches suffices for a percolation phase transition, yielding survival of contact processes with periodic recovery.
Brochette percolation
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Oriented bond-site percolation in random environment and contact processes with periodic recovery
For oriented bond-site percolation with columnar stretches, a (1+ε)-moment condition on stretches suffices for a percolation phase transition, yielding survival of contact processes with periodic recovery.