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

Abstract : 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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https://hal.archives-ouvertes.fr/hal-01696417
Contributor : Cristina Toninelli <>
Submitted on : Tuesday, January 30, 2018 - 1:51:16 PM
Last modification on : Friday, April 10, 2020 - 5:26:45 PM
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  • HAL Id : hal-01696417, version 1

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

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