About a nonideal Rayleigh gas mixture model

TL;DR

This paper develops a generalized grand canonical mixture model for nonideal Rayleigh gases, analyzing correlation functions and convergence properties to establish a law of large numbers and improve convergence rates.

Contribution

It introduces a novel grand canonical mixture model for nonideal Rayleigh gases, extending correlation analysis and convergence results with phase space perturbations.

Findings

Proved a law of large numbers for the system.

Extended correlation function analysis to all orders.

Improved convergence rates using adaptive time cutting.

Abstract

This paper introduces a grand canonical mixture model to generalize the nonideal Rayleigh gas [5] to an asymptotically infinite amount of perturbed tagged particles. This model relies precisely on grand canonical tags, to preserve symmetry in the system, contrary to [2]. We hence define and study the convergence of the correlation functions of this system in large times, linking it to the expectancy of the empirical measure of tagged and non-tagged particles, to eventually prove a law of large numbers for this dynamics. We extend the quantitative study to all the correlation functions, and not only the first one, exhibiting the resultant additional factors, and we also generalize the perturbation to the whole phase space, instead of considering a space-only initial perturbation. Eventually, we fit our adaptive time cutting [12] to the mixture system, even improving it to get better convergence rates.