Fluctuation bounds in the exponential bricklayers process

Details Fluctuation bounds in the exponential bricklayers process Fluctuation bounds in the exponential bricklayers process

2011-07-24

arxiv.org/abs/1107.4752v2

Mathematics

Probability

34 pages, revised version after referees comments, accepted at JSP. A few explanations added, some proofs shortened in the App

Scientific paper

10.1007/s10955-012-0470-5

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.

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