Rates of divergence of non-conventional ergodic averages
نویسندگان
چکیده
منابع مشابه
Rates of Divergence of Nonconventional Ergodic Averages
We study the rate of growth of ergodic sums along a sequence (an) of times: SNf(x) = ∑ n≤N f(T nx). We characterize the maximal rate of growth and identify a number of sequences such as an = 2, along which the maximal rate of growth is achieved. We also return to Khintchine’s Strong Uniform Distribution Conjecture that the averages (1/N) ∑ n≤N f(nx mod 1) converge pointwise to ∫ f for integrabl...
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We study convergence of Markov chains {Xk} to their stationary distributions π(·). Much recent work has used coupling to get quantitative bounds on the total variation distance between the law L(Xn) and π(·). In this paper, we use shift-coupling to get quantitative bounds on the total variation distance between the ergodic average law 1 n n ∑ k=1 L(Xk) and π(·). This avoids certain problems, re...
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The case l = 1 is the mean ergodic theorem, and the result can be viewed as a generalization of that theorem. The l = 2 case was proven by Conze and Lesigne [Conze and Lesigne, 1984], and various special cases for higher l have been shown by Zhang [Zhang, 1996], Frantzikinakis and Kra [Frantzikinakis and Kra, 2005], Lesigne [Lesigne, 1993], and Host and Kra [Host and Kra, 2005]. Tao’s argument ...
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متن کاملErgodic averages with deterministic weights
i.e., there exists a constant C such that SN(θ, u) ≤ CN . We define δ(θ, u) to be the infimum of the δ satisfying H1 for θ and u. About H1, in the case where θ takes its values in U (the set of complex numbers of modulus 1), it is clear that for all sequences θ and u, δ(θ, u) is smaller than or equal to 1 and it is well-known (see [Ka] for example) that it is greater than or equal to 1/2. Few e...
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ژورنال
عنوان ژورنال: Ergodic Theory and Dynamical Systems
سال: 2009
ISSN: 0143-3857,1469-4417
DOI: 10.1017/s0143385709000054