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May 2021 New lower bounds for trace reconstruction
Zachary Chase
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Ann. Inst. H. Poincaré Probab. Statist. 57(2): 627-643 (May 2021). DOI: 10.1214/20-AIHP1089

Abstract

We improve the lower bound on worst case trace reconstruction from Ω(n5/4logn) to Ω(n3/2log7n). As a consequence, we improve the lower bound on average case trace reconstruction from Ω(log9/4nloglogn) to Ω(log5/2n(loglogn)7).

Nous améliorons la borne inférieure, dans le cas pire, de la reconstruction par trace de Ω(n5/4logn) à Ω(n3/2log7n). Comme conséquence, nous améliorons la borne inférieure, dans le cas moyenné, de la reconstruction par trace de Ω(log9/4nloglogn) à Ω(log5/2n(loglogn)7).

Acknowledgements

I would like to thank Omer Tamuz for introducing me to the wonderful trace reconstruction problem, and for helpful discussions. I would also like to thank Russell Lyons for much helpful feedback on the paper, and for a bijective proof of Lemma 1. Finally, I would like to greatly thank an anonymous referee for several helpful comments, substantially improving the paper’s readability and understandability.

Citation

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Zachary Chase. "New lower bounds for trace reconstruction." Ann. Inst. H. Poincaré Probab. Statist. 57 (2) 627 - 643, May 2021. https://doi.org/10.1214/20-AIHP1089

Information

Received: 13 November 2019; Revised: 13 April 2020; Accepted: 16 July 2020; Published: May 2021
First available in Project Euclid: 13 May 2021

Digital Object Identifier: 10.1214/20-AIHP1089

Subjects:
Primary: 62B10

Keywords: statistics

Rights: Copyright © 2021 Association des Publications de l’Institut Henri Poincaré

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Vol.57 • No. 2 • May 2021
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