On a coloured tree with non i.i.d. random labels

Skevi Michael (1) , Stanislav Volkov (1)

1 Department of Mathematics [Bristol]

We obtain new results for the probabilistic model introducedin [3] and [4] which involves a -ary regular tree. All vertices are coloured in one of distinct colours so that children of each vertex all have different colours. Fix strictly positive random variables. For any two connected vertices of the tree assign to the edge between them which has the same distribution as one of these random variables, such that the distribution is determined solely by the colours of its endpoints. of a vertex is defined as a product of all labels on the path connecting the vertex to the root. We study how the total number of vertices with value of at least grows as , and apply the results to some other relevant models.

Mots clés: Physical Sciences

Domaines: Bio-informatique [q-bio.QM]; Bio-Informatique, Biologie Systémique [q-bio.QM]

Skevi Michael, Stanislav Volkov. On a coloured tree with non i.i.d. random labels. Statistics and Probability Letters, 2010, 80 (23-24), pp.1896. ⟨10.1016/j.spl.2010.08.017⟩. ⟨hal-00691776⟩