Supplementary material with detailed explanations of statements and conclusion proposed in "Random Walk for modelling Multi Core Fiber cross-talk and step distribution characterisation" by A. Ottino et al.<div><br></div><div>It includes mathematical derivation of original phase shift for every core pair, proof that the proposed model converges to the most widely used in literature and analytical and Monte-Carlo characterisation of IC-XT step distribution.</div><div><br></div><div>This information provides better insight and understanding of the work proposed in the respective manuscript</div><div><br></div>