The analyticity region of the hard sphere gas. Improved bounds

TL;DR

This paper improves the bounds on the analyticity region of the pressure in the hard-sphere gas model across dimensions, notably increasing the known estimates for two-dimensional cases.

Contribution

It provides new, numerically computed bounds for the radius of analyticity of the pressure in the hard-sphere gas, surpassing classical estimates especially in two dimensions.

Findings

Estimated the radius of analyticity is about 40% larger in 2D.

Used numerical computation of multidimensional regions to determine bounds.

Provided improved bounds applicable across multiple dimensions.

Abstract

We find an improved estimate of the radius of analyticity of the pressure of the hard-sphere gas in $d$ dimensions. The estimates are determined by the volume of multidimensional regions that can be numerically computed. For $d=2$, for instance, our estimate is about 40% larger than the classical one.