  Intermittent maps of Pomeau-Manneville type are well-studied in
one-dimension, and also in higher dimensions if the map happens to be Markov.
In general, the nonconformality of multidimensional intermittent maps
represents a challenge that up to now is only partially addressed. We show how
to prove sharp polynomial bounds on decay of correlations for a class of
multidimensional intermittent maps. In addition we show that the optimal
results on statistical limit laws for one-dimensional intermittent maps hold
also for the maps considered here. This includes the (functional) central limit
theorem and local limit theorem, Berry-Esseen estimates, large deviation
estimates, convergence to stable laws and L\'evy processes, and infinite
measure mixing.
