Growing Cayley trees described by Fermi distribution

TL;DR

This paper presents a model for growing Cayley trees influenced by thermal noise, revealing that bond energy distributions follow Fermi statistics and connecting these results to scale-free networks described by Bose statistics.

Contribution

It introduces a novel model linking Cayley tree growth with Fermi distribution and explores its relation to other network models like Eden and Invasion Percolation.

Findings

Bond energy distribution follows Fermi statistics.

Model reduces to Eden and Invasion Percolation models at temperature limits.

Connects Fermi and Bose statistics in network growth models.

Abstract

We introduce a model for growing Cayley trees with thermal noise. The evolution of these hierarchical networks reduces to the Eden model and the Invasion Percolation model in the limit $T\to 0$, $T\to \infty$ respectively. We show that the distribution of the bond strengths (energies) is described by the Fermi statistics. We discuss the relation of the present results with the scale-free networks described by Bose statistics.