Before revision:  The proof makes use of a classical supermartingale result, and also rewrites the algorithm as a sequence of random continuous operators in the primal-dual space. We compare our analysis with a similar argument by Alacaoglu et al., and give sufficient conditions for an unproven claim in their proof .
After revision:  We also look into its application to parallel Magnetic Resonance Imaging reconstruction in order to test performance of SPDHG. Our numerical results show that for a range of settings SPDHG converges significantly faster than its deterministic counterpart .