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.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.This information provides better insight and understanding of the work proposed in the respective manuscript