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Determinantal structure of the 1D asymmetric exclusion process and KPZ fluctuations
Abstract Book of the XXIII IUPAP International Conference on Statistical Physics, Genova, Italy, (9-13 July 2007)
Аннотация
The one-dimensional asymmetric simple exclusion process
(ASEP) is a stochastic process of many particles in
which each particle performs the asymmetric random walk
on a chain under the volume exclusion effect. Due to the
nonlinear and noise effects, the ASEP shows a lot of interesting
phenomena characteristic of systems far from equilibrium.
At the same time the ASEP has several beautiful mathematical
structures. Among them is a determinantal formula of
the Green's function by Schuetz. This has further
turned out to be related to the free-fermion nature of the
ASEP which is not apparent in the definition of the process.
This allows us to study various time dependent properties
of the model and hence to obtain detailed information
on the scaling behaviors of the Kardar-Parisi-Zhang(KPZ)
universality class. An application is the exact computation
of the spatial correlations of the particle currents for
certain initial conditions. They are described by what we
call the Airy processes. The connections to some
combinatorial problems and random matrix theory are also
discussed.
