A random model of publication activity

TL;DR

This paper introduces a random model for publication activity with weighted objects, demonstrating convergence and scale-free properties using martingale theory and renewal equations.

Contribution

It generalizes existing random graph models and provides rigorous proofs of convergence and scale-free behavior in weighted object evolution.

Findings

Proves almost sure convergence of weight distribution

Shows scale-free asymptotic behavior

Uses martingale and renewal theory in proofs

Abstract

We examine a random model consisting of objects with positive weights and evolving in discrete time steps, which generalizes certain random graph models. We prove almost sure convergence for the weight distribution and show scale-free asymptotic behaviour. Martingale theory and renewal-like equations are used in the proofs.