  We investigate theoretically the low energy physics of semiconductor Majorana
wires in the vicinity of a magnetic field-driven topological quantum phase
transition (TQPT). The local density of states (LDOS) at the end of the wire,
which is directly related to the differential conductance in the limit of
point-contact tunneling, is calculated numerically. We find that the dependence
of the end-of-wire LDOS on the magnetic field is non-universal and that the
signatures associated with the closing of the superconducting gap at the
Majorana TQPT are essentially invisible within a significant range of
experimentally relevant parameters. Our results provide an explanation for the
recent observation of the apparent non-closure of the gap at the Majorana TQPT
in semiconductor nanowires.
