Analytic nonregular cocycles over irrational rotations

Mariusz Lemańczyk

Displaying similar documents to “Analytic nonregular cocycles over irrational rotations”

The rearrangement inequality for the ergodic maximal function.

Ephremidze, L. (2001)

Georgian Mathematical Journal

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Another proof of Derriennic's reverse maximal inequality for the supremum of ergodic ratios

Ryotaro Sato (2006)

Commentationes Mathematicae Universitatis Carolinae

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Using the ratio ergodic theorem for a measure preserving transformation in a $σ$ -finite measure space we give a straightforward proof of Derriennic’s reverse maximal inequality for the supremum of ergodic ratios.

Continuous subadditive processes and formulae for Lyapunov characteristic exponents

Wojciech Słomczyński (1995)

Annales Polonici Mathematici

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Asymptotic properties of various semidynamical systems can be examined by means of continuous subadditive processes. To investigate such processes we consider different types of exponents: characteristic, central, singular and global exponents and we study their properties. We derive formulae for central and singular exponents and show that they provide upper bounds for characteristic exponents. The concept of conjugate processes introduced in this paper allows us to find lower bounds...

Doubly stochastic operators on a finite-dimensional simplex.

Shahidi, F.A. (2009)

Sibirskij Matematicheskij Zhurnal

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On a relationship between the integrabilities of various maximal functions.

Ephremidze, L. (1995)

Georgian Mathematical Journal

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A note on prediction for discrete time series

Gusztáv Morvai, Benjamin Weiss (2012)

Kybernetika

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Let ${X_{n}}$ be a stationary and ergodic time series taking values from a finite or countably infinite set $𝒳$ and that $f (X)$ is a function of the process with finite second moment. Assume that the distribution of the process is otherwise unknown. We construct a sequence of stopping times $λ_{n}$ along which we will be able to estimate the conditional expectation $E (f (X_{λ_{n} + 1}) | X_{0}, \dots, X_{λ_{n}})$ from the observations $(X_{0}, \dots, X_{λ_{n}})$ in a point wise consistent way for a restricted class of stationary and ergodic finite or countably infinite alphabet...

Ergodicity for piecewise smooth cocycles over toral rotations

Anzelm Iwanik (1998)

Fundamenta Mathematicae

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Let α be an ergodic rotation of the d-torus $𝕋^{d} = ℝ^{d} / ℤ^{d}$ . For any piecewise smooth function $f : 𝕋^{d} \to ℝ$ with sufficiently regular pieces the unitary operator Vh(x) = exp(2π if(x))h(x + α) acting on $L^{2} (𝕋^{d})$ is shown to have a continuous non-Dirichlet spectrum if the gradient of f has nonzero integral. In particular, the resulting skew product $S_{f} : 𝕋^{d + 1} \to 𝕋^{d + 1}$ must be ergodic. If in addition α is sufficiently well approximated by rational vectors and f is represented by a linear function with noninteger coefficients then the spectrum...

Ergodic averages and free $ℤ^{2}$ actions

Zoltán Buczolich (1999)

Fundamenta Mathematicae

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If the ergodic transformations S, T generate a free $ℤ^{2}$ action on a finite non-atomic measure space (X,S,µ) then for any $c_{1}, c_{2} \in ℝ$ there exists a measurable function f on X for which ${(N + 1)}^{- 1} \sum_{j = 0}^{N} f (S^{j} x) \to c_{1}$ and ${(N + 1)}^{- 1} \sum_{j = 0}^{N} f (T^{j} x) \to c_{2} µ$ -almost everywhere as N → ∞. In the special case when S, T are rationally independent rotations of the circle this result answers a question of M. Laczkovich.

Uniqueness of the stationary distribution and stabilizability in Zhang's sandpile model.

Boer, Anne Fey-Den, Liu, Haiyan, Meester, Ronald (2009)

Electronic Journal of Probability [electronic only]

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