text: 146,104,1479430336035672066,213005784,Josué Tonelli-Cueto,First preprint of 2022 is out! New bounds for the best rank-one approx. ratio of [partially] symmetric tensors—aka [multi]homogeneus polynomials—using probability. <LINK> #research #math #paper #preprint #tensors #polynomials #approximaton #probability #arxiv @_pbrdng Out of an e-mail asking Khazhgali if a probabilistic technique in another paper would be interesting in the world of symmetric tensors.,https://arxiv.org/abs/2201.02191,"We provide new upper and lower bounds on the minimum possible ratio of the spectral and Frobenius norms of a (partially) symmetric tensor. In the particular case of general tensors our result recovers a known upper bound. For symmetric tensors our upper bound unveils that the ratio of norms has the same order of magnitude as the trivial lower bound $1/\sqrt{n^{d-1}}$, when the order of a tensor $d$ is fixed and the dimension of the underlying vector space $n$ tends to infinity. However, when $n$ is fixed and $d$ tends to infinity, our lower bound is better than $1/\sqrt{n^{d-1}}$. ",Probabilistic bounds on best rank-one approximation ratio,2,"['First preprint of 2022 is out! New bounds for the best rank-one approx. ratio of [partially] symmetric tensors—aka [multi]homogeneus polynomials—using probability.\n\n<LINK>\n\n#research #math #paper #preprint #tensors #polynomials #approximaton #probability\n#arxiv', '@_pbrdng Out of an e-mail asking Khazhgali if a probabilistic technique in another paper would be interesting in the world of symmetric tensors.']",22,01,404