Logarithmic Sobolev inequality for the inhomogeneous zero range process

TL;DR

This paper establishes that the logarithmic Sobolev constant for the inhomogeneous zero range process scales as the square of the system size, providing insights into the system's mixing properties and spectral gap.

Contribution

It proves the growth rate of the logarithmic Sobolev constant for inhomogeneous zero range processes, extending understanding of their functional inequalities.

Findings

Logarithmic Sobolev constant grows as N^2 for the process.

Results apply to inhomogeneous systems with applications to colored particle systems.

Enhances understanding of mixing times and spectral properties.

Abstract

We prove that the logarithmic Sobolev constant for the inhomogeneous symmetric nearest neighbour zero range process on a cube of size N^d grows as N^2. We apply this result to the inhomogeneous process which arises in the study of the homogeneous version of the zero range interacting particle system with colours.