Microscopic concavity and fluctuation bounds in a class of deposition processes

Balázs, Márton; Komjáthy, Júlia; Seppäläinen, Timo

Annales de l'I.H.P. Probabilités et statistiques, Tome 48 (2012) no. 1, pp. 151-187.

Nous démontrons des bornes sur les fluctuations du courant de particules pour des processus de zero-range unidimensionnels totalement asymétriques avec des taux de sauts concaves dont la pente décroît exponentiellement. Les fluctuations dans la direction des caractéristiques sont de l'ordre t1/3 en accord avec les prédictions de la classe d'universalité de KPZ. Notre résultat est obtenu par un raisonnement robuste qui est formulé pour une classe importante de processus de déposition. Au-delà du processus de zero-range, les hypothèses de notre argument ont aussi été vérifiées dans des articles antérieurs pour le processus d'exclusion simple asymétrique et le processus de zero-range avec taux constants. Ces hypothèses sont en cours de développement pour un processus de déposition avec des taux de sauts dont la croissance est exponentielle.

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 t1/3. 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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