- Autor
- Berkes, István
- Borda, Bence
- TitelOn the law of the iterated logarithm for random exponential sums
- Datei
- LicenceCC BY
- Download Statistik1438
- Peer ReviewNein
- AbstractThe asymptotic behavior of exponential sums \(Σ^N_{k=1} exp(2πin_k α)\) for Hadamard lacunary \((n_k )\) is well known, but for general \((n_k )\) very few precise results exist, due to number theoretic difficulties. It is therefore natural to consider random \((n_k )\) and in this paper we prove the law of the iterated logarithm for \(Σ^N_{k=1} exp(2πin_k α)\) if the gaps \(n_{k+1} − n_k\) are independent, identically distributed random variables. As a comparison, we give a lower bound for the discrepancy of \(\{n_k α\}\) under the same random model, exhibiting a completely different behavior.
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