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Weak dependence for a class of local functionals of Markov chains on \(\mathbb Z^d\). (English) Zbl 1363.60014

The authors consider a random walk in a dynamical random environment with mutual interaction introduced by C. Boldrighini et al. [Ann. Inst. Henri Poincare, Probab. Stat. 30, No. 4, 519-558, 559–605 (1994; Zbl 0818.60063, Zbl 0818.60064)]. For this model, they prove a central limit theorem for sequences \(\{ f(S^k\hat{\eta})\}_{k=0}^\infty\), where \(S\) is the time shift, \(f\) is strictly local in space and belongs to a class of functionals related to the Hölder continuous functions on the torus, \(\hat{\eta}=\{ \eta_t\}_{t=0}^\infty\) is a Markov chain on \(\mathbb Z^d\).

MSC:

60F05 Central limit and other weak theorems
60J10 Markov chains (discrete-time Markov processes on discrete state spaces)
60J35 Transition functions, generators and resolvents
60G50 Sums of independent random variables; random walks
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