PreprintarXiv licencearXiv
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).
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BibTeX
@misc{leppanen2026decay,
title = {{Decay of correlations and normal approximation for nonstationary heterochaos baker maps}},
author = {Juho Leppänen and Hiroki Takahasi},
howpublished = {arXiv},
year = {2026},
month = aug,
doi = {10.48550/arxiv.2608.29135},
eprint = {2608.29135},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2608.29135},
}
RIS
TY - UNPB
TI - Decay of correlations and normal approximation for nonstationary heterochaos baker maps
AU - Juho Leppänen
AU - Hiroki Takahasi
PY - 2026
DA - 2026/08/29
PB - arXiv
DO - 10.48550/arxiv.2608.29135
UR - https://arxiv.org/abs/2608.29135
AB - 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).
ER -