  We study products of precursors of spatially local operators,
$W_{x_{n}}(t_{n}) ... W_{x_1}(t_1)$, where $W_x(t) = e^{-iHt} W_x e^{iHt}$.
Using chaotic spin-chain numerics and gauge/gravity duality, we show that a
single precursor fills a spatial region that grows linearly in $t$. In a
lattice system, products of such operators can be represented using tensor
networks. In gauge/gravity duality, they are related to Einstein-Rosen bridges
supported by localized shock waves. We find a geometrical correspondence
between these two descriptions, generalizing earlier work in the spatially
homogeneous case.
