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

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.