Bose-Einstein condensation in random directed networks

TL;DR

This paper investigates Bose-Einstein condensation phenomena in a dynamic directed network model where vertices and edges are added probabilistically, influenced by fitness distributions, leading to condensation under certain conditions.

Contribution

It introduces a model of a growing directed network incorporating fitness-dependent attachment rates and analyzes the conditions for Bose-Einstein condensation.

Findings

Condensation occurs depending on the fitness distribution f(a,b)

The model captures phase transition behavior in network growth

Provides a framework linking quantum phenomena to network theory

Abstract

We consider the phenomenon of Bose-Einstein condensation in a random growing directed network. The network grows by the addition of vertices and edges. At each time step the network gains a vertex with probabilty $p$ and an edge with probability $1-p$. The new vertex has a fitness $(a,b)$ with probability $f(a,b)$. A vertex with fitness $(a,b)$, in-degree $i$ and out-degree $j$ gains a new incoming edge with rate $a(i+1)$ and an outgoing edge with rate $b(j+1)$. The Bose-Einstein condensation occurs as a function of fitness distribution $f(a,b)$.