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

Sharp Statistical Properties for a Family of Multidimensional NonMarkovian Nonconformal Intermittent Maps