2 research outputs found
Microscopic concavity and fluctuation bounds in a class of deposition processes
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 . 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.Comment: Improved after Referee's comments: we added explanations and changed
some parts of the text. 50 pages, 1 figur
A pedestrian's view on interacting particle systems, KPZ universality, and random matrices
These notes are based on lectures delivered by the authors at a Langeoog
seminar of SFB/TR12 "Symmetries and universality in mesoscopic systems" to a
mixed audience of mathematicians and theoretical physicists. After a brief
outline of the basic physical concepts of equilibrium and nonequilibrium
states, the one-dimensional simple exclusion process is introduced as a
paradigmatic nonequilibrium interacting particle system. The stationary measure
on the ring is derived and the idea of the hydrodynamic limit is sketched. We
then introduce the phenomenological Kardar-Parisi-Zhang (KPZ) equation and
explain the associated universality conjecture for surface fluctuations in
growth models. This is followed by a detailed exposition of a seminal paper of
Johansson that relates the current fluctuations of the totally asymmetric
simple exclusion process (TASEP) to the Tracy-Widom distribution of random
matrix theory. The implications of this result are discussed within the
framework of the KPZ conjecture.Comment: 52 pages, 4 figures; to appear in J. Phys. A: Math. Theo