  Many applications such as recommendation systems or sports tournaments
involve pairwise comparisons within a collection of $n$ items, the goal being
to aggregate the binary outcomes of the comparisons in order to recover the
latent strength and/or global ranking of the items. In recent years, this
problem has received significant interest from a theoretical perspective with a
number of methods being proposed, along with associated statistical guarantees
under the assumption of a suitable generative model.
  While these results typically collect the pairwise comparisons as one
comparison graph $G$, however in many applications - such as the outcomes of
soccer matches during a tournament - the nature of pairwise outcomes can evolve
with time. Theoretical results for such a dynamic setting are relatively
limited compared to the aforementioned static setting. We study in this paper
an extension of the classic BTL (Bradley-Terry-Luce) model for the static
setting to our dynamic setup under the assumption that the probabilities of the
pairwise outcomes evolve smoothly over the time domain $[0,1]$. Given a
sequence of comparison graphs $(G_{t'})_{t' \in \mathcal{T}}$ on a regular grid
$\mathcal{T} \subset [0,1]$, we aim at recovering the latent strengths of the
items $w_t^* \in \mathbb{R}^n$ at any time $t \in [0,1]$. To this end, we adapt
the Rank Centrality method - a popular spectral approach for ranking in the
static case - by locally averaging the available data on a suitable
neighborhood of $t$. When $(G_{t'})_{t' \in \mathcal{T}}$ is a sequence of
Erd\"os-Renyi graphs, we provide non-asymptotic $\ell_2$ and $\ell_{\infty}$
error bounds for estimating $w_t^*$ which in particular establishes the
consistency of this method in terms of $n$, and the grid size
$\lvert\mathcal{T}\rvert$. We also complement our theoretical analysis with
experiments on real and synthetic data.
