  We suggest a non-asymptotic matrix perturbation-theoretic approach to get
sharp bounds on the expected meeting time of random walks on large (possibly
random) graphs. We provide a formula for the expected meeting time in terms of
the singular value decomposition of the diagonally killed generator of a pair
of independent random walks, which we view as a perturbation of the generator.
Employing a rank-one approximation of the diagonally killed generator as the
proof of concept, we work out sharp bounds on the expected meeting time of
simple random walks on sufficiently dense Erd\H{o}s-R\'enyi random graphs.
