  We study the validity of the large-N equivalence between four-dimensional
SU(N) lattice gauge theory and its momentum quenched version--the Quenched
Eguchi-Kawai (QEK) model. We find that the assumptions needed for the proofs of
equivalence do not automatically follow from the quenching prescription. We use
weak-coupling arguments to show that large-N equivalence is in fact likely to
break down in the QEK model, and that this is due to dynamically generated
correlations between different Euclidean components of the gauge fields. We
then use Monte-Carlo simulations at intermediate couplings with 20 <= N <= 200
to provide strong evidence for the presence of these correlations and for the
consequent breakdown of reduction. This evidence includes a large discrepancy
between the transition coupling of the "bulk" transition in lattice gauge
theories and the coupling at which the QEK model goes through a strongly
first-order transition. To accurately measure this discrepancy we adapt the
recently introduced Wang-Landau algorithm to gauge theories.
