  We provide a statistical framework for characterizing stochastic particle
production in the early universe via a precise correspondence to current
conduction in wires with impurities. Our approach is particularly useful when
the microphysics is uncertain and the dynamics are complex, but only
coarse-grained information is of interest. We study scenarios with multiple
interacting fields and derive the evolution of the particle occupation numbers
from a Fokker-Planck equation. At late times, the typical occupation numbers
grow exponentially which is the analog of Anderson localization for disordered
wires. Some statistical features of the occupation numbers show hints of
universality in the limit of a large number of interactions and/or a large
number of fields. For test cases, excellent agreement is found between our
analytic results and numerical simulations.
