LOCAL LIMIT THEOREMS FOR PARTIAL SUMS OF STATIONARY SEQUENCES GENERATED BY GIBBS–MARKOV MAPS

By J. Aaronson, Manfred Denker. 2001

247 citations recorded by the source corpus.

Subfields: Computational Theory and Mathematics, Geometry and Topology, Mathematical Physics

View Paper: https://www.semanticscholar.org/paper/c33f0b52c0a2a0b08d693901b3a286a1f4e90987

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Citations in the corpus

Central limit theorem and stable laws for intermittent maps (2002, methodology): “s gives h= ψ◦T−ψ. Central limit theorem and stable laws for intermittent maps 29 3.4 The classical method: stable laws case The following theorem has essentially been proved by Aaronson and Denker in [AD01]. Theorem 3.8. Let (Z,B,T,m,δ) be a Markov map preserving the ﬁnite ergodic measure m. We assu”
Berry-Esseen theorem and local limit theorem for non uniformly expanding maps (2003, background): “This paragraph is related to the end of Section 3 of [3].”
Sharp polynomial estimates for the decay of correlations (2002, background): “dulus, the ergodicity of Tγ gives that |f| is constant almost everywhere, hence everywhere by continuity. As f≡ 0, this constant is nonzero, and we get e−itϕγ = f/f◦ T γ. We can apply Theorem 3.1. in [AD01] and obtain that fis δ∗-measurable, where δ∗ is the smallest partition such that 26 S.Gou¨ezel”
Annealed and quenched limit theorems for random expanding dynamical systems (2013, methodology): “This can be checked using known techniques, see [1, 2, 17] among many others for more details.”
Existence of gibbs measures for countable Markov shifts (2003, result): “This follows from the results in section 2 in [3] (see theorem 4.”
Operator renewal theory and mixing rates for dynamical systems with infinite measure (2010, methodology): “In our situation, the key is to use the fact that the return time ϕ lies in the domain of a stable law, and a Nagaev-type argument due to Aaronson & Denker [4] shows that (1 − λ(θ))−1 ∼ const ℓ(1/θ)−1θ−β when β ∈ (0, 1).”
From rates of mixing to recurrence times via large deviations (2010, unknown): “is adapted to L1(m). On the space L the Perron-Frobenius operator satisﬁes the Lasota-Yorke inequality and the density of the invariant measure will be m-almost everywhere bounded away from zero; see [AD]. B.3. Multidimensional maps. The third interesting example is given by multidimensional piecewi”