Precise asymptotics for a variable-range hopping model

For a system of localised electron states the DC conductivity vanishes at zero temperature, but localised electrons can conduct at finite - temperature. Mott gave a theory for the low-temperature conductivity in terms of a variable-range hopping model, which is hard to analyse. Here we give precise asymptotic results for a modified variable-range hopping model, proposed by S. Alexander [Phys. Rev. B 26 (1982), 2956]