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We establish two open problems from Kesten and Sidoravicius (Kesten and Sidoravicius, 2006). Particles are initially placed on Z d with a given density and evolve as independent continuous-time random walks. Particles initially placed at the origin are declared as infected. Infection transmits instantaneously to healthy particles on the same site and infected particles become healthy with a positive rate. We prove that, for small enough recovery rates, the infection process survives and visits the origin infinitely many times on the event of survival. Second, we establish the existence of density parameters for which the infection survives for all choices of the recovery rate.
|Number of pages||13|
|Journal||Stochastic Processes and their Applications|
|Early online date||14 Mar 2023|
|Publication status||E-pub ahead of print - 14 Mar 2023|
- 60K37, 60K35, 82C22
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