Fluctuation bounds in the exponential bricklayers process

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; Industry Sectors