Trees with product-form random weights

Abstract

We consider growing random recursive trees in random environment, in which at each step a new vertex is attached according to a probability distribution that assigns the tree vertices masses proportional to their random weights.The main aim of the paper is to study the asymptotic behavior of the mean numbers of outgoing vertices as the number of steps tends to infinity, under the assumption that the random weights have a product form with independent identically distributed factors.

Keywords

• random recursive trees
• random environment
• sptizer's condition
• distance to the root
• outdegrees
• [info.info-ds] computer science [cs]/data structures and algorithms [cs.ds]
• [info.info-dm] computer science [cs]/discrete mathematics [cs.dm]
• [math.math-co] mathematics [math]/combinatorics [math.co]