WIAS Preprint No. 3047, (2023)

A long-range contact process in a random environment


  • Jahnel, Benedikt
    ORCID: 0000-0002-4212-0065
  • Vu, Anh Duc
    ORCID: 0009-0005-6913-4992

2020 Mathematics Subject Classification

  • 60K35 60K37


  • Contact process, space-time random environment, long-range directed percolation, phase transition, multiscale renormalization




We study survival and extinction of a long-range infection process on a diluted one-dimensional lattice in discrete time. The infection can spread to distant vertices according to a Pareto distribution, however spreading is also prohibited at random times. We prove a phase transition in the recovery parameter via block arguments. This contributes to a line of research on directed percolation with long-range correlations in nonstabilizing random environments.

Download Documents