This is an announcement for the paper "The multiplicative property characterizes $\ell_p$ and $L_p$ norms" by Guillaume Aubrun and Ion Nechita. Abstract: We show that $\ell_p$ norms are characterized as the unique norms which are both invariant under coordinate permutation and multiplicative with respect to tensor products. Similarly, the $L_p$ norms are the unique rearrangement-invariant norms on a probability space such that $\|X Y\|=\|X\|\cdot\|Y\|$ for every pair $X,Y$ of independent random variables. Our proof relies on Cram\'er's large deviation theorem. Archive classification: math.FA Remarks: 8 pages, 1 figure Submitted from: inechita@uottawa.ca The paper may be downloaded from the archive by web browser from URL http://front.math.ucdavis.edu/1102.2618 or http://arXiv.org/abs/1102.2618