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Microscopic concavity and fluctuation bounds in a class of deposition processes. (English. French summary) Zbl 1247.82039
The paper addresses anomalous current fluctuations of attractive interacting systems in one dimension, with one conserved quantity, specifically the hydrodynamic flux function which determines the $$t$$-scaling. The paper focuses on the $$1/3$$ exponent and makes a further step towards establishing the universality of $$t^{1/3}$$-order fluctuations, by rewriting an earlier proof for the asymmetric simple exclusion process (ASEP) and the constant rate totally asymmetric zero range process (TAZRP) in a fairly general way. A crucial feature that underlies scaling proofs connected with these models is named microscopic concavity property. Considered as a hypothesis, this property may be interpreted as an input that relaxes otherwise very rigid earlier proofs of the $$t^{1/3}$$ scaling. Three subclasses of processes are identified to respect this property, e.g., ASEP, TAZRP and the totally asymmetric bricklayers process with convex exponential jump rate. The authors expect the validity of the above-mentioned hypothesis for a broader class of totally asymmetric concave zero range processes, because its key part can be directly verified and only a certain tail estimate is missing (to be examined in case of a specific model).

##### MSC:
 82C22 Interacting particle systems in time-dependent statistical mechanics 60K35 Interacting random processes; statistical mechanics type models; percolation theory 82C24 Interface problems; diffusion-limited aggregation in time-dependent statistical mechanics
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