Random self-similar trees and a hierarchical branching process

Multifractal spectra for random self-similar measures via branching processes

Abstract Start with a compact set K ⊂ Rd. This has a random number of daughter sets each of which is a (rotated and scaled) copy of K and all of which are inside K. The random mechanism for producing daughter sets is used independently on each of the daughter sets to produce the second generation of sets, and so on, repeatedly. The random fractal set F is the limit, as n goes to infinity, of th...

Self-similar branching Markov chains

The main purpose of this work is to study self-similar branching Markov chains. First we will construct such a process. Then we will establish certain Limit Theorems using the theory of self-similar Markov processes.

Self-similar hierarchical honeycombs

References 2.full.html#ref-list-1 http://rspa.royalsocietypublishing.org/content/469/2156/2013002 This article cites 34 articles, 8 of which can be accessed free Subject collections (164 articles) mechanical engineering • Articles on similar topics can be found in the following collections Email alerting service here the box at the top right-hand corner of the article or click Receive free ema...

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...