Berkes, István and Borda, Bence (2018) Berry–Esseen Bounds and Diophantine Approximation. ANALYSIS MATHEMATICA, 44 (2). pp. 149-161. ISSN 0133-3852
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Abstract
Let SN, N = 1, 2,.. be a random walk on the integers, let α be an irrational number and let ZN = {SNα>}, where {·} denotes fractional part. Then ZN, N = 1, 2,.. is a random walk on the circle, and from classical results of probability theory it follows that the distribution of ZN converges weakly to the uniform distribution. We determine the precise speed of convergence, which, in addition to the distribution of the elementary step X of the random walk SN, depends sensitively on the rational approximation properties of α. © 2018, Akadémiai Kiadó, Budapest, Hungary.
| Item Type: | Article |
|---|---|
| Uncontrolled Keywords: | Weak convergence; i.i.d. sums mod 1; Diophantine approximation; Convergence speed |
| Subjects: | Q Science / természettudomány > QA Mathematics / matematika |
| SWORD Depositor: | MTMT SWORD |
| Depositing User: | MTMT SWORD |
| Date Deposited: | 12 Sep 2018 10:28 |
| Last Modified: | 12 Sep 2018 10:28 |
| URI: | http://real.mtak.hu/id/eprint/83655 |
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