On a coloured tree with non i.i.d. random labels
We obtain new results for the probabilistic model introduced in Menshikov et al. (2007) and Volkov (2006) which involves a dd-ary regular tree. All vertices are coloured in one of dd distinct colours so that dd children of each vertex all have different colours. Fix d2d2 strictly positive random variables. For any two connected vertices of the tree assign to the edge between them a label which has
