  The hierarchical SVD provides a quasi-best low rank approximation of high
dimensional data in the hierarchical Tucker framework. Similar to the SVD for
matrices, it provides a fundamental but expensive tool for tensor computations.
In the present work we examine generalizations of randomized matrix
decomposition methods to higher order tensors in the framework of the
hierarchical tensors representation. In particular we present and analyze a
randomized algorithm for the calculation of the hierarchical SVD (HSVD) for the
tensor train (TT) format.
