  We show non-asymptotic exponential convergence of Sinkhorn iterates to the
Schr\"odinger potentials, solutions of the quadratic Entropic Optimal Transport
problem on $\mathbb{R}^d$. Our results hold under mild assumptions on the
marginal inputs: in particular, we only assume that they admit an
asymptotically positive log-concavity profile, covering as special cases
log-concave distributions and bounded smooth perturbations of quadratic
potentials. Up to the authors' knowledge, these are the first results which
establish exponential convergence of Sinkhorn's algorithm in a general setting
without assuming bounded cost functions or compactly supported marginals.
