Fluctuation bounds in the exponential bricklayers process

TL;DR

This paper demonstrates that the totally asymmetric exponential bricklayers process exhibits t^{1/3}-order current fluctuations, supporting the universality of this scaling in models with convex hydrodynamics.

Contribution

It extends previous results to include a model with convex hydrodynamics, confirming the universality of fluctuation scaling in such systems.

Findings

First example with convex hydrodynamics showing t^{1/3} fluctuations

Supports universality of fluctuation scaling across different models

Confirms assumptions for exponential bricklayers process

Abstract

This paper is the continuation of our earlier paper, where we proved t^{1/3}-order of current fluctuations across the characteristics in a class of one dimensional interacting systems with one conserved quantity. We also claimed two models with concave hydrodynamic flux which satisfied the assumptions which made our proof work. In the present note we show that the totally asymmetric exponential bricklayers process also satisfies these assumptions. Hence this is the first example with convex hydrodynamics of a model with t^{1/3}-order current fluctuations across the characteristics. As such, it further supports the idea of universality regarding this scaling.