  In this work, we estimate the number of randomly selected elements of a
tensor that with high probability guarantees local convergence of Riemannian
gradient descent for tensor train completion. We derive a new bound for the
orthogonal projections onto the tangent spaces based on the harmonic mean of
the unfoldings' singular values and introduce a notion of core coherence for
tensor trains. We also extend the results to tensor train completion with
auxiliary subspace information and obtain the corresponding local convergence
guarantees.
