István Berkes
Current Organizations / Institutes
The organizations/institutes from the scholar's latest article
Previous Organizations / Institutes
The organizations / institutes from the scholar's other articles in the past ten years
Research Subjects
István Berkes has a total of 37 co-authors. Here are the top co-authors by number of shared publications:
- Robert F. Tichy
Institute of Analysis and Number Theory, Graz University of Technology, Graz, Austria
14 shared publications - Christoph Aistleitner
Graz University of Technology Institute of Analysis and Number Theory Steyrergasse 30 8010 Graz Austria
10 shared publications - Michel Weber
IRMA, UMR 7501 , Strasbourg Cedex , France
5 shared publications - Lajos Horváth
University of Utah
4 shared publications - Christoph Aistleitner
Graz University of Technology
3 shared publications Lajos Horváth
University of Utah
3 shared publications
Latest Publications
- Open Access
- 31 March 2026
- Published by Springer Nature in BMC Musculoskeletal Disorders
- Vol. 27 (1)
Arthroscopic primary repair of the anterior cruciate ligament with internal brace ligament augmentation: a viable alternative to reconstruction? A systematic literature review and analysis
Primary anterior cruciate ligament (ACL) repair has re-gained significant interest due to its inherent anatomic advantages: retaining the proprioceptive fi
- 31 March 2026
- Published by Springer Nature in BMC Musculoskeletal Disorders
- Vol. 27 (1)
Open AccessArthroscopic primary repair of the anterior cruciate ligament with internal brace ligament augmentation: a viable alternative to reconstruction? A systematic literature review and analysis
Primary anterior cruciate ligament (ACL) repair has re-gained significant interest due to its inherent anatomic advantages: retaining the proprioceptive fi
- Open Access
- 1 December 2019
- Published by Walter de Gruyter GmbH in Uniform distribution theory
- Vol. 14 (2) , 73-86
On the Discrepancy of Random Walks on the Circle
Let X1,X2,... be i.i.d. absolutely continuous random variables, let(mod 1) and let D*N denote the star discrepancy of the sequence (Sk)1≤k≤N. We determine the limit distribution of and the weak limit of the sequence in the Skorohod space D[0, 1], where FN (t) denotes the empirical distribution function of the sequence (Sk)1≤k≤N. - 1 December 2019
- Published by Walter de Gruyter GmbH in Uniform distribution theory
- Vol. 14 (2) , 73-86
Open AccessOn the Discrepancy of Random Walks on the Circle
Let X1,X2,... be i.i.d. absolutely continuous random variables, let(mod 1) and let D*N denote the star discrepancy of the sequence (Sk)1≤k≤N. We determine the limit distribution of and the weak limit of the sequence in the Skorohod space D[0, 1], where FN (t) denotes the empirical distribution function of the sequence (Sk)1≤k≤N. - 13 June 2018
- Published by Springer Nature in Analysis Mathematica
- Vol. 44 (2) , 149-161
Berry–Esseen Bounds and Diophantine Approximation
- 13 June 2018
- Published by Springer Nature in Analysis Mathematica
- Vol. 44 (2) , 149-161
Berry–Esseen Bounds and Diophantine Approximation
- Open Access
- 1 March 2018
- Published by Akademiai Kiado Zrt. in Studia Scientiarum Mathematicarum Hungarica
- Vol. 55 (1) , 141-152
ON TRIGONOMETRIC SUMS WITH RANDOM FREQUENCIES
We prove that if I-k are disjoint blocks of positive integers and n(k) are independent random variables on some probability space (Omega, F, P) such that nk is uniformly distributed on I-k, then N-1/2 Sigma(N)(k=1)(sin 2 pi n(k)x - E(sin 2 pi n(k)x)) has, with P-probability 1, a mixed Gaussian limit distribution relative to the probability space ((0,1), B, lambda), where B is the Borel sigma-algebra and lambda is the Lebesgue measure. We also investigate the case when n(k) have continuous uniform distribution on disjoint intervals I-k on the positive axis.
- 1 March 2018
- Published by Akademiai Kiado Zrt. in Studia Scientiarum Mathematicarum Hungarica
- Vol. 55 (1) , 141-152
Open AccessON TRIGONOMETRIC SUMS WITH RANDOM FREQUENCIES
We prove that if I-k are disjoint blocks of positive integers and n(k) are independent random variables on some probability space (Omega, F, P) such that nk is uniformly distributed on I-k, then N-1/2 Sigma(N)(k=1)(sin 2 pi n(k)x - E(sin 2 pi n(k)x)) has, with P-probability 1, a mixed Gaussian limit distribution relative to the probability space ((0,1), B, lambda), where B is the Borel sigma-algebra and lambda is the Lebesgue measure. We also investigate the case when n(k) have continuous uniform distribution on disjoint intervals I-k on the positive axis.
- Open Access
On permutation-invariance of limit theorems
By a classical principle of probability theory, sufficiently thin subsequences of general sequences of random variables behave like i.i.d.\ sequences. This observation not only explains the remarkable properties of lacunary trigonometric series, but also provides a powerful tool in many areas of analysis, such the theory of orthogonal series and Banach space theory. In contrast to i.i.d.\ sequences, however, the probabilistic structure of lacunary sequences is not permutation-invariant and the analytic properties of such sequences can change after rearrangement. In a previous paper we showed that permutation-invariance of subsequences of the trigonometric system and related function systems is connected with Diophantine properties of the index sequence. In this paper we will study permutation-invariance of subsequences of general r.v.\ sequences.
Open AccessOn permutation-invariance of limit theorems
By a classical principle of probability theory, sufficiently thin subsequences of general sequences of random variables behave like i.i.d.\ sequences. This observation not only explains the remarkable properties of lacunary trigonometric series, but also provides a powerful tool in many areas of analysis, such the theory of orthogonal series and Banach space theory. In contrast to i.i.d.\ sequences, however, the probabilistic structure of lacunary sequences is not permutation-invariant and the analytic properties of such sequences can change after rearrangement. In a previous paper we showed that permutation-invariance of subsequences of the trigonometric system and related function systems is connected with Diophantine properties of the index sequence. In this paper we will study permutation-invariance of subsequences of general r.v.\ sequences.
- Open Access
Lacunary series and stable distributions
By well known results of probability theory, any sequence of random variables with bounded second moments has a subsequence satisfying the central limit theorem and the law of the iterated logarithm in a randomized form. In this paper we give criteria for a sequence $(X_n)$ of random variables to have a subsequence $(X_{n_k})$ whose weighted partial sums, suitably normalized, converge weakly to a stable distribution with parameter $0<\alpha<2$.Open AccessLacunary series and stable distributions
By well known results of probability theory, any sequence of random variables with bounded second moments has a subsequence satisfying the central limit theorem and the law of the iterated logarithm in a randomized form. In this paper we give criteria for a sequence $(X_n)$ of random variables to have a subsequence $(X_{n_k})$ whose weighted partial sums, suitably normalized, converge weakly to a stable distribution with parameter $0<\alpha<2$. - Open Access
- 30 May 2017
- Published by Springer Nature
- p. 137-167
On the Uniform Theory of Lacunary Series
- 30 May 2017
- Published by Springer Nature
- p. 137-167
Open AccessOn the Uniform Theory of Lacunary Series
- Open Access
- 26 May 2017
- Published by Springer Nature in Monatshefte für Mathematik
- Vol. 186 (3) , 393-406
Strong approximation of lacunary series with random gaps
- 26 May 2017
- Published by Springer Nature in Monatshefte für Mathematik
- Vol. 186 (3) , 393-406
Open AccessStrong approximation of lacunary series with random gaps
- Open Access
- 28 November 2016
- Published by Taylor & Francis in Statistics
- Vol. 51 (1) , 3-10
Strong approximation of the St. Petersburg game
Let be i.i.d. random variables with and let . The properties of the sequence have received considerable attention in the literature in connection with the St. Petersburg paradox (Bernoulli 1738). Let be a semistable Lévy process with underlying Lévy measure . For a suitable version of and , we prove the strong approximation a.s. This provides the first example for a strong approximation theorem for partial sums of i.i.d. sequences not belonging to the domain of attraction of the normal or stable laws.- 28 November 2016
- Published by Taylor & Francis in Statistics
- Vol. 51 (1) , 3-10
Open AccessStrong approximation of the St. Petersburg game
Let be i.i.d. random variables with and let . The properties of the sequence have received considerable attention in the literature in connection with the St. Petersburg paradox (Bernoulli 1738). Let be a semistable Lévy process with underlying Lévy measure . For a suitable version of and , we prove the strong approximation a.s. This provides the first example for a strong approximation theorem for partial sums of i.i.d. sequences not belonging to the domain of attraction of the normal or stable laws. - Open Access
- 24 October 2016
- Published by Springer Nature in Acta Mathematica Hungarica
- Vol. 151 (1) , 199-216
A metric discrepancy result with given speed
- 24 October 2016
- Published by Springer Nature in Acta Mathematica Hungarica
- Vol. 151 (1) , 199-216
Open AccessA metric discrepancy result with given speed