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Microscopic concavity and fluctuation bounds in a class of deposition processes

Márton BalázsJúlia KomjáthyTimo Seppäläinen — 2012

Annales de l'I.H.P. Probabilités et statistiques

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 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....

Modeling flocks and prices: Jumping particles with an attractive interaction

Márton BalázsMiklós Z. RáczBálint Tóth — 2014

Annales de l'I.H.P. Probabilités et statistiques

We introduce and investigate a new model of a finite number of particles jumping forward on the real line. The jump lengths are independent of everything, but the jump rate of each particle depends on the relative position of the particle compared to the center of mass of the system. The rates are higher for those left behind, and lower for those ahead of the center of mass, providing an attractive interaction keeping the particles together. We prove that in the fluid limit, as the number of particles...

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