Microscopic concavity and fluctuation bounds in a class of deposition processes

TL;DR

This paper establishes fluctuation bounds for particle currents in a class of one-dimensional deposition processes, demonstrating KPZ universality and providing a robust framework applicable to various related models.

Contribution

It introduces a broad, robust method to derive fluctuation bounds for deposition processes with concave jump rates, extending previous results to new classes of models.

Findings

Fluctuations in characteristic directions are of order t^{1/3}.

Results align with KPZ universality class expectations.

Method applies to multiple deposition-type processes.

Abstract

We prove fluctuation bounds for the particle current in totally asymmetric zero range processes in one dimension with nondecreasing, concave jump rates whose slope decays exponentially. Fluctuations in the characteristic directions have order of magnitude $t^{1/3}$. This is in agreement with the expectation that these systems lie in the same KPZ universality class as the asymmetric simple exclusion process. The result is via a robust argument formulated for a broad class of deposition-type processes. Besides this class of zero range processes, hypotheses of this argument have also been verified in the authors' earlier papers for the asymmetric simple exclusion and the constant rate zero range processes, and are currently under development for a bricklayers process with exponentially increasing jump rates.