WIAS Preprint No. 3095, (2024)

An ergodic and isotropic zero-conductance model with arbitrarily strong local connectivity


  • Heida, Martin
    ORCID: 0000-0002-7242-8175
  • Jahnel, Benedikt
    ORCID: 0000-0002-4212-0065
  • Vu, Anh Duc
    ORCID: 0009-0005-6913-4992

2020 Mathematics Subject Classification

  • 60K35 60K37 60G55 90B18


  • Homogenisation, percolation, randomly stretched lattice, conductivity




We exhibit a percolating ergodic and isotropic lattice model in all but at least two dimensions that has zero effective conductivity in all spatial directions and for all non-trivial choices of the connectivity parameter. The model is based on the so-called randomly stretched lattice where we additionally elongate layers containing few open edges.

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