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arXiv · 2608.29135

Decay of correlations and normal approximation for nonstationary heterochaos baker maps

Juho Leppänen·Hiroki Takahasi
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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).

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Juho Leppänen, Hiroki Takahasi. 2026-08-29. Decay of correlations and normal approximation for nonstationary heterochaos baker maps. https://arxiv.org/abs/2608.29135

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