  We consider the low-energy region of an array of Luttinger liquids coupled by
a weak interchain hopping. The leading logarithmic divergences can be re-summed
to all orders within a self-consistent perturbative expansion in the hopping,
in the large-dimension limit. The anomalous exponent scales to zero below the
one-particle crossover temperature. As a consequence, coherent quasiparticles
with finite weight appear along the whole Fermi surface. Extending the
expansion self-consistently to all orders turns out to be crucial in order to
restore the correct Fermi-liquid behavior.
