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              <p>For Hénon maps, Bianchi and Dinh recently proved the exponential mixing of all orders for the measure of maximal entropy and, as a consequence of the recent work of Björklund and Gorodnik, the CLT for Hölder observables. We extend their results to generic birational maps of $\mathbb{P}^k$. Because of the indeterminacy set, Hölder maps are not stable under iteration, so we need to work with a suitable space of test functions.</p>
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