Microscopic concavity and fluctuation bounds in a class of deposition processes

Details Microscopic concavity and fluctuation bounds in a class of deposition processes Microscopic concavity and fluctuation bounds in a class of deposition processes

2008-08-08

arxiv.org/abs/0808.1177v3

Annales de L'Institut Henri Poincare-Probabilites Et Statistiques 48:(1) pp. 151-187. (2012)

Mathematics

Probability

Improved after Referee's comments: we added explanations and changed some parts of the text. 50 pages, 1 figure

Scientific paper

10.1214/11-AIHP415

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.

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