  Boson sampling is the problem of generating a quantum bit stream whose
average is the permanent of a $n\times n$ matrix. The bitstream is created as
the output of a prototype quantum computing device with $n$ input photons. It
is a fundamental challenge to verify boson sampling, and the question of how
output count rates scale with matrix size $n$ is crucial. Here we apply results
from random matrix theory to establish scaling laws for average count rates in
boson sampling experiments with arbitrary inputs and losses. The results show
that, even with losses included, verification of nonclassical behaviour at
large $n$ values is indeed possible.
