Microscopic concavity and fluctuation bounds in a class of deposition processes

Abstract

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.

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

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• Total Current Fluctuations in ASEP
• Weakly Asymmetric Non-Simple Exclusion Process and the Kardar-Parisi-Zhang Equation
• A q-weighted version of the Robinson-Schensted algorithm
• Non-existence of bi-infinite geodesics in the exponential corner growth model
• Generalizations of TASEP in discrete and continuous inhomogeneous space
• A Multi-species ASEP(q,j) and q-TAZRP with Stochastic Duality
• Joint distribution of Busemann functions in the exactly solvable corner growth model
• Optimal-order exit point bounds in exponential last-passage percolation via the coupling technique
• On the asymmetric zero-range in the rarefaction fan
• Product blocking measures and a particle system proof of the Jacobi triple product
• Fluctuation bounds in the exponential bricklayers process
• Q-zero range has random walking shocks
• Tail estimates for the stationary stochastic six vertex model and ASEP
• Point Fields of Last Passage Percolation and Coalescing Fractional Brownian Motions