We improve the lower bound on worst case trace reconstruction from to . As a consequence, we improve the lower bound on average case trace reconstruction from to .
Nous améliorons la borne inférieure, dans le cas pire, de la reconstruction par trace de à . Comme conséquence, nous améliorons la borne inférieure, dans le cas moyenné, de la reconstruction par trace de à .
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.
"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