# Practical criteria for R-positive recurrence of unbounded semigroups

## TL;DR

This paper leverages recent advances in quasi-stationary distributions to establish practical criteria ensuring geometric convergence of normalized unbounded semigroups, simplifying the analysis of their long-term behavior.

## Contribution

It introduces new, easily applicable criteria for R-positive recurrence of unbounded semigroups based on quasi-stationary distribution theory.

## Key findings

- Derived general criteria for geometric convergence
- Simplified analysis of unbounded semigroup behavior
- Enhanced understanding of R-positive recurrence

## Abstract

The goal of this note is to show how recent results on the theory of quasi-stationary distributions allow to deduce effortlessly general criteria for the geometric convergence of normalized unbounded semigroups.