  A matrix model describing surfaces embedded in a Bethe lattice is considered.
From the mean field point of view, it is equivalent to the Kazakov-Migdal
induced gauge theory and therefore, at $N=\infty$ and $d>1$, the latter can be
interpreted as a matrix model for infinite-tension strings. We show that, in
the naive continuum limit, it is governed by the one-matrix-model saddle point
with an upside-down potential. To derive mean field equations, we consider the
one-matrix model in external field. As a simple application, its explicit
solution in the case of the inverted W potential is given.
