Current fluctuations for stochastic particle systems with drift in one spatial dimension

✍ Scribed by Timo Seppäläinen

Publisher: Sociedade Brasileira de Matemática
Year: 2010
Tongue: English
Leaves: 81
Series: Ensaios Matemáticos 18
Category: Library

No coin nor oath required. For personal study only.

✦ Synopsis

Abstract. This review article discusses limit distributions and variance
bounds for particle current in several dynamical stochastic systems of particles
on the one-dimensional integer lattice: independent particles, independent
particles in a random environment, the random average process,
the asymmetric simple exclusion process, and a class of totally asymmetric
zero range processes. The first three models possess linear macroscopic
flux functions and lie in the Edwards-Wilkinson universality class with
scaling exponent 1/4 for current fluctuations. For these we prove Gaussian
limits for the current process. The latter two systems belong to the
Kardar-Parisi-Zhang class. For these we prove the scaling exponent 1/3 in
the form of upper and lower variance bounds.

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