  We explore consequences of the existence of gluonic hot spots inside the
proton for coherent and incoherent exclusive vector meson production cross
sections in deep inelastic scattering. By working in the dilute limit of the
Color Glass Condensate framework to compute the cross sections for Gaussian hot
spots of fluctuating color charges and employing a non-relativistic vector
meson wave function, we are able to perform large parts of the calculation
analytically. We find that the coherent cross section is sensitive to both the
size of the target and the structure of the probe. The incoherent cross section
is dominated by color fluctuations at small transverse momentum transfer ($t$),
by proton and hot spot sizes as well as the structure of the probe at medium
$t$ and again by color fluctuations at large $t$. While the $t$-dependence of
the cross section is well reproduced in our model, the relative normalization
between the coherent and the incoherent cross sections points to the need for
additional fluctuations in the proton.
