Decay of correlations and normal approximation for nonstationary heterochaos baker maps

Abstract

We study statistical properties of nonstationary compositions of a sequence of heterochaos baker maps. For maps whose central direction is mostly expanding, we establish three main results: exponential rate of memory loss for a broad class of measures (Theorem 1.1), a functional correlation bound with stretched exponential decay (Theorem 1.2), and an error bound for the multivariate central limit theorem (CLT) in the Wasserstein-1 distance (Theorem 1.3). The proofs are based on the construction of suitable Gibbs--Markov induced maps for the nonstationary compositions. In a certain special case we obtain a concrete estimate on the rate of convergence in the multivariate CLT (Theorem 1.4).