Random trees with superexponential branching weights

Random Trees with Superexponential Branching Weights

We study rooted planar random trees with a probability distribution which is proportional to a product of weight factors wn associated to the vertices of the tree and depending only on their individual degrees n. We focus on the case when wn grows faster than exponentially with n. In this case the measures on trees of finite size N converge weakly as N tends to infinity to a measure which is co...

Recursive random trees with product-form random weights

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 th...

Search Trees and Branching Random Walks

Random trees and general branching processes

We consider a tree that grows randomly in time. Each time a new vertex appears, it chooses exactly one of the existing vertices and attaches to it. The probability that the new vertex chooses vertex x is proportional to w(deg(x)), a weight function of the actual degree of x. The weight function w : N → R+ is the parameter of the model. In [4] and [11] the authors derive the asymptotic degree di...

Disassortativity of random critical branching trees.

Random critical branching trees (CBTs) are generated by the multiplicative branching process, where the branching number is determined stochastically, independent of the degree of their ancestor. Here we show analytically that despite this stochastic independence, there exists the degree-degree correlation (DDC) in the CBT and it is disassortative. Moreover, the skeletons of fractal networks, t...