The one dimensional asymmetric zero-range process (ZRP) whose macroscopic particle flux is a strictly convex or concave function of particle density is expected to be a member of the Kardar-Parisi-Zhang (KPZ) universality class. In particular, this entails that an observer who moves at the characteristic speed should observe fluctuations of order t^{1/3} in the net particle current. This talk describes a probabilistic coupling proof of the 1/3 fluctuation exponent. The proof relies on precise control of discrepancy particles and works for totally asymmetric ZRP whose jump rate function is concave with exponentially decaying slope.

This is joint work with Márton Balázs (Bristol) and Komjáthy Júlia (Eindhoven).

Timo Seppalainen (Wisconsin)Wed, Feb 3

The one dimensional asymmetric zero-range process (ZRP) whose macroscopic particle flux is a strictly convex or concave function of particle density is expected to be a member of the Kardar-Parisi-Zhang (KPZ) universality class. In particular, this entails that an observer who moves at the characteristic speed should observe fluctuations of order t^{1/3} in the net particle current. This talk describes a probabilistic coupling proof of the 1/3 fluctuation exponent. The proof relies on precise control of discrepancy particles and works for totally asymmetric ZRP whose jump rate function is concave with exponentially decaying slope.

This is joint work with Márton Balázs (Bristol) and Komjáthy Júlia (Eindhoven).