Phase transition for a non attractive process modeling inherited sterility

Velasco Sonia, Université Paris Cité

We introduce an interacting particle system which models the inherited sterility method, widely used for pest control. Individuals evolve on Zd according to a contact process of parameter λ. With probability p ∈ [0, 1] an offspring is fertile and can give birth to other individuals at rate λ. With probability 1 − p, an offspring is sterile and blocks the site it sits on until it dies. The goal is to prove that for certain values of λ, the system exhibits a phase transition in the parameter p. The model is not attractive, since an increase of fertile individuals potentially causes that of sterile ones. Usual methods for phase transition results are therefore no longer valid. We overcome this difficulty by using a comparison argument with an attractive model for which these methods hold.

Area: CS18 - Interacting systems in statistical physics II (Chiara Franceschini and Elena Magnanini)

Keywords: Contact process, phase transition, percolation

Please Login in order to download this file