  Solving high-dimensional dynamical systems in multi-query or real-time
applications requires efficient surrogate modelling techniques, as e.g.,
achieved via model order reduction (MOR). If these systems are Hamiltonian
systems their physical structure should be preserved during the reduction,
which can be ensured by applying symplectic basis generation techniques such as
the complex SVD (cSVD). Recently, randomized symplectic methods such as the
randomized complex singular value decomposition (rcSVD) have been developed for
a more efficient computation of symplectic bases that preserve the Hamiltonian
structure during MOR. In the current paper, we present two error bounds for the
rcSVD basis depending on the choice of hyperparameters and show that with a
proper choice of hyperparameters, the projection error of rcSVD is at most a
constant factor worse than the projection error of cSVD. We provide numerical
experiments that demonstrate the efficiency of randomized symplectic basis
generation and compare the bounds numerically.
