# A correction to a remark in a paper by Procacci and Yuhjtman: new lower bounds for the convergence radius of the virial series

## TL;DR

This paper establishes a new, more accurate lower bound for the convergence radius of the virial series in classical particle systems, correcting previous overestimations and improving upon classical bounds.

## Contribution

It provides a rigorously proven lower bound for the virial series convergence radius, refining earlier estimates and correcting prior claims in the literature.

## Key findings

- New lower bound for the virial series convergence radius
- Correction of previous overestimated bounds
- Improvement over classical Lebowitz-Penrose estimate

## Abstract

In this note we deduce a new lower bound for the convergence radius of the Virial series of a continuous system of classical particles interacting via a stable and tempered pair potential using the estimates on the Mayer coefficients obtained in the recent paper by Procacci and Yuhjtman (Lett Math Phys 107:31-46, 2017). This corrects the wrongly optimistic lower bound for the same radius claimed (but not proved) in the above cited paper (in Remark 2 below Theorem 1). The lower bound for the convergence radius of the Virial series provided here represents a strong improvement on the classical estimate given by Lebowitz and Penrose in 1964.