# Fluctuation Bounds in the Exponential Bricklayers Process

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## Abstract

This paper is the continuation of our earlier paper (Balázs et al. in Ann. Inst. Henri Poincaré Probab. Stat. 48(1):151–187, 2012), 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.

## Keywords

Interacting particle systems Universal fluctuation bounds*t*

^{1/3}-Scaling Second class particle Convexity Bricklayers process

## Notes

### Acknowledgements

M. Balázs and J. Komjáthy were partially supported by the Hungarian Scientific Research Fund (OTKA) grants K100473, K60708, TS49835, F67729, and the Morgan Stanley Mathematical Modeling Center. M. Balázs was also supported by the Bolyai Scholarship of the Hungarian Academy of Sciences. T. Seppäläinen was partially supported by National Science Foundation grants DMS-0701091 and DMS-10-03651, and by the Wisconsin Alumni Research Foundation.

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