Ergodic Theory.

Intro -- Contents -- Preface -- Injectivity of the Dubins-Freedman construction of random distributions -- A maximal inequality for the tail of the bilinear Hardy-Littlewood function -- Almost sure convergence of weighted sums of independent random variables -- Recurrence, ergodicity and invariant measures for cocycles over a rotation -- 1. Invariant measures, regularity of a cocycle -- 2. Growth of the ergodic sums over a rotation, application to recurrence -- 3. Examples of ergodic BV Rd-cocycles -- 4. Examples of non-regular cocycles -- 5. Appendix : A diophantine property for (α, β) -- References -- Examples of recurrent or transient stationary walks in Rd over a rotation of T2 -- 1. A sufficient condition of recurrence for stationary walks -- 2. Series with small denominators -- 3. Growth in norm ll ll2 of the ergodic sums and recurrence -- 4. An example of transient cocycle -- References -- A short proof of the unique ergodicity of horocyclic flows -- Aperiodic order via dynamical systems: Diffraction for sets of finite local complexity -- Laws of iterated logarithm for weighted sums of iid random variables -- Homeomorphic Bernoulli trial measures and ergodic theory -- Distinguishing transformations by averaging methods -- Some open problems.

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Electronic reproduction. Ann Arbor, Michigan : ProQuest Ebook Central, 2024. Available via World Wide Web. Access may be limited to ProQuest Ebook Central affiliated libraries.