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Article Dans Une Revue Markov Processes And Related Fields Année : 2018

PHASE TRANSITION FOR A NON-ATTRACTIVE INFECTION PROCESS IN HETEROGENEOUS ENVIRONMENT

Marinus Gottschau
  • Fonction : Auteur
Markus Heydenreich
  • Fonction : Auteur
Kilian Matzke
  • Fonction : Auteur

Résumé

We consider a non-attractive three state contact process on Z and prove that there exists a regime of survival as well as a regime of extinction. In more detail, the process can be regarded as an infection process in a dynamic environment, where non-infected sites are either healthy or passive. Infected sites can recover only if they have a healthy site nearby, whereas non-infected sites may become infected only if there is no healthy and at least one infected site nearby. The transition probabilities are governed by a global parameter q: for large q, the infection dies out, and for small enough q, we observe its survival. The result is obtained by a coupling to a discrete time Markov chain, using its drift properties in the respective regimes.
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Dates et versions

hal-01696417 , version 1 (30-01-2018)

Identifiants

  • HAL Id : hal-01696417 , version 1

Citer

Marinus Gottschau, Markus Heydenreich, Kilian Matzke, Cristina Toninelli. PHASE TRANSITION FOR A NON-ATTRACTIVE INFECTION PROCESS IN HETEROGENEOUS ENVIRONMENT. Markov Processes And Related Fields, 2018. ⟨hal-01696417⟩
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