  We prove several fundamental statistical bounds for entropic OT with the
squared Euclidean cost between subgaussian probability measures in arbitrary
dimension. First, through a new sample complexity result we establish the rate
of convergence of entropic OT for empirical measures. Our analysis improves
exponentially on the bound of Genevay et al. (2019) and extends their work to
unbounded measures. Second, we establish a central limit theorem for entropic
OT, based on techniques developed by Del Barrio and Loubes (2019). Previously,
such a result was only known for finite metric spaces. As an application of our
results, we develop and analyze a new technique for estimating the entropy of a
random variable corrupted by gaussian noise.
