The law of the iterated logarithm for discrepancies of \(\{\theta^{n}x\}\)
From MaRDI portal
Publication:950344
DOI10.1007/s10474-007-6201-8zbMath1241.11090OpenAlexW1968831457MaRDI QIDQ950344
Publication date: 22 October 2008
Published in: Acta Mathematica Hungarica (Search for Journal in Brave)
Full work available at URL: https://doi.org/10.1007/s10474-007-6201-8
Strong limit theorems (60F15) Irregularities of distribution, discrepancy (11K38) Lacunary series of trigonometric and other functions; Riesz products (42A55)
Related Items (38)
A metric discrepancy result for lacunary sequences ⋮ Metric discrepancy results for subsequences of geometric progressions ⋮ Large deviation principles for lacunary sums ⋮ Metric discrepancy results for geometric progressions with large ratios ⋮ Metric discrepancy results for alternating geometric progressions ⋮ On the central limit theorem for \(f(n_{k}x)\) ⋮ Insertion in constructed normal numbers ⋮ Metric discrepancy results for geometric progressions with small ratios ⋮ On the Uniform Theory of Lacunary Series ⋮ Diophantine equations and the LIL for the discrepancy of sublacunary sequences ⋮ On the law of the iterated logarithm for trigonometric series with bounded gaps ⋮ Metric discrepancy results for geometric progressions with large ratios. II ⋮ On the class of limits of lacunary trigonometric series ⋮ Limit distributions in metric discrepancy theory ⋮ A metric discrepancy result for a lacunary sequence with small gaps ⋮ Metric discrepancy results for geometric progressions perturbed by irrational rotations ⋮ Normal Numbers and Computer Science ⋮ A metric discrepancy result for the sequence of powers of minus two ⋮ Quantitative uniform distribution results for geometric progressions ⋮ Metric discrepancy results for subsequences of \(\{\theta^k x\}\) ⋮ A metric discrepancy result with given speed ⋮ A metric discrepancy result for the Hardy-Littlewood-Pólya sequences ⋮ Irregular discrepancy behavior of lacunary series ⋮ A law of the iterated logarithm for discrepancies: non-constant limsup ⋮ Irregular discrepancy behavior of lacunary series. II ⋮ Normal numbers and nested perfect necklaces ⋮ On the law of the iterated logarithm for the discrepancy of lacunary sequences ⋮ The central limit theorem for complex Riesz-Raikov sums ⋮ The law of the iterated logarithm for the discrepancy of perturbed geometric progressions ⋮ On the law of the iterated logarithm for permuted lacunary sequences ⋮ METRIC RESULTS ON THE DISCREPANCY OF SEQUENCES MODULO ONE FOR INTEGER SEQUENCES OF POLYNOMIAL GROWTH ⋮ PROBABILITY AND METRIC DISCREPANCY THEORY ⋮ On the law of the iterated logarithm for the discrepancy of \(\langle n_kx\rangle\) ⋮ On permutations of Hardy-Littlewood-Pólya sequences ⋮ Convergence of $∑c_{k} f(k x)$ and the Lip $𝛼$ class ⋮ On the law of the iterated logarithm for the discrepancy of lacunary sequences II ⋮ The law of the iterated logarithm for the discrepancies of a permutation of \(\{n_kx\}\) ⋮ Extremal discrepancy behavior of lacunary sequences
Cites Work
- A functional law of the iterated logarithm for empirical distribution functions of weakly dependent random variables
- On the asymptotic behaviour of ?f(nkx)
- Mixing sequences of random variables and probablistic number theory
- Limit theorems for lacunary series and uniform distribution mod 1
- The central limit theorem for Riesz-Raikov sums
- The central limit theorem for Riesz-Raikov sums
This page was built for publication: The law of the iterated logarithm for discrepancies of \(\{\theta^{n}x\}\)
