Abstract polymer gas. A simple inductive proof of the Fern\'andez-Procacci criterion

TL;DR

This paper presents a straightforward inductive proof of the Fernández-Procacci criterion, simplifying the understanding of convergence conditions for cluster expansions in abstract polymer gases.

Contribution

It introduces a new, simpler inductive proof method for the Fernández-Procacci criterion, enhancing theoretical understanding.

Findings

Provides a more accessible proof of the criterion

Simplifies the theoretical framework for convergence analysis

Potentially facilitates further research in polymer gas models

Abstract

This note contains an alternative proof of the Fern\'andez-Procacci criterion for the convergence of cluster expansion on the abstract polymer gas via a simple inductive argument a l\'a Dobrushin.