$A+A \to A$, $\; \; B+A \to A$

TL;DR

This paper studies the decay of particle intensities in a two-species diffusing and reacting system on a lattice, showing how diffusion and reaction rates affect polynomial decay in high dimensions.

Contribution

It demonstrates that particle intensities approximately follow modified rate equations, revealing the influence of diffusion and reaction rates on decay in supercritical dimensions.

Findings

Particle intensities decay polynomially over time.

Decay rates are influenced by underlying diffusion and reaction parameters.

System behavior aligns with modified rate equations in high dimensions.

Abstract

This paper considers the decay in particle intensities for a translation invariant two species system of diffusing and reacting particles on $\mathbb{Z}^d$ for $d \geq 3$. The intensities are shown to approximately solve modified rate equations, from which their polynomial decay can be deduced. The system illustrates that the underlying diffusion and reaction rates can influence the exact polynomial decay rates, despite the system evolving in a supercritical dimension.