  Recently a novel large-N reduction has been proposed as a maximally
supersymmetric regularization of N=4 super Yang-Mills theory on RxS^3 in the
planar limit. This proposal, if it works, will enable us to study the theory
non-perturbatively on a computer, and hence to test the AdS/CFT correspondence
analogously to the recent works on the D0-brane system. We provide a nontrivial
check of this proposal by performing explicit calculations in the large-N
reduced model, which is nothing but the so-called plane wave matrix model,
around a particular stable vacuum corresponding to RxS^3. At finite temperature
and at weak coupling, we reproduce precisely the deconfinement phase transition
in the N=4 super Yang-Mills theory on RxS^3. This phase transition is
considered to continue to the strongly coupled regime, where it corresponds to
the Hawking-Page transition on the AdS side. We also perform calculations
around other stable vacua, and reproduce the phase transition in super
Yang-Mills theory on the corresponding curved space-times such as RxS^3/Z_q and
RxS^2.
