  Path-integral methods can be used to derive a `path-decomposition expansion'
for the temperature Green function of a magnetized free-electron gas confined
by a hard wall. With the help of this expansion the asymptotic behaviour of the
profiles for the excess particle density and the electric current density far
from the edge is determined for arbitrary values of the magnetic field
strength. The asymptotics are found to depend sensitively on the degree of
degeneracy. For a non-degenerate electron gas the asymptotic profiles are
essentially Gaussian (albeit modulated by a Bessel function), on a length scale
that is a function of the magnetic field strength and the temperature. For a
completely degenerate electron gas the asymptotic behaviour is again
proportional to a Gaussian, with a scale that is the magnetic length in this
case. The prefactors are polynomial and logarithmic functions of the distance
from the wall, that depend on the number of filled Landau levels $n$. As a
consequence, the Gaussian asymptotic decay sets in at distances that are large
compared to the magnetic length multiplied by $\sqrt{n}$.
