Geodesic
The analytic rank of tensors and its applications
Discrete analysis (2019) Cet article a éte moissonné depuis la source Scholastica

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The analytic rank of a tensor, first defined by Gowers and Wolf in the context of higher-order Fourier analysis, is defined to be the logarithm of the bias of the tensor. We prove that it is a subadditive measure of rank: that is, the analytic rank of the sum of two tensors is at most the sum of their individual analytic ranks. This analytic property turns out to have surprising applications: (i) common roots of tensors are always positively correlated; and (ii) the slice rank and partition rank, which were defined recently in the resolution of the cap-set problem in Ramsey theory, can be replaced by the analytic rank.
Publié le : 
@article{DAS_2019_a13,
     author = {Shachar Lovett},
     title = {The analytic rank of tensors and its applications},
     journal = {Discrete analysis},
     year = {2019},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/DAS_2019_a13/}
}
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JO  - Discrete analysis
PY  - 2019
UR  - http://geodesic.mathdoc.fr/item/DAS_2019_a13/
LA  - en
ID  - DAS_2019_a13
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%0 Journal Article
%A Shachar Lovett
%T The analytic rank of tensors and its applications
%J Discrete analysis
%D 2019
%U http://geodesic.mathdoc.fr/item/DAS_2019_a13/
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Shachar Lovett. The analytic rank of tensors and its applications. Discrete analysis (2019). http://geodesic.mathdoc.fr/item/DAS_2019_a13/