Analytical and numerical studies of creation probabilities of hierarchical trees

TL;DR

This paper investigates the creation probabilities of various hierarchical trees using analytical and numerical methods, emphasizing the role of deformed algebra in establishing a consistent probabilistic framework.

Contribution

It introduces a novel approach linking hierarchical level creation probabilities with their integration into a unified structure, utilizing deformed algebra.

Findings

Analytical results for regular and degenerate trees.

Numerical determination of creation probabilities for Fibonacci, scale-free, and arbitrary trees.

Highlighting the necessity of deformed algebra for a consistent probabilistic description.

Abstract

We consider the creation conditions of diverse hierarchical trees both analytically and numerically. A connection between the probabilities to create hierarchical levels and the probability to associate these levels into a united structure is studied. We argue that a consistent probabilistic picture requires the use of deformed algebra. Our consideration is based on the study of the main types of hierarchical trees, among which both regular and degenerate ones are studied analytically, while the creation probabilities of Fibonacci, scale-free and arbitrary trees are determined numerically.