Disassortativity of random critical branching trees

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...

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...

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...

Anisotropic Branching Random Walks on Homogeneous Trees

Symmetric branching random walk on a homogeneous tree exhibits a weak survival phase: For parameter values in a certain interval, the population survives forever with positive probability, but, with probability one, eventually vacates every finite subset of the tree. In this phase, particle trails must converge to the geometric boundary of the tree. The random subset 3 of the boundary consisti...