1112.0873 (Tobias Galla)

Fluctuations in meta-population exclusion processes    [PDF]

Tobias Galla

We introduce a meta-population version of models of asymmetric exclusion
models, consisting of a spatial arrangement of patches. Patches are of a
specific size, indicating the maximal number of particles they can hold. We use
an expansion in the inverse patch size to calculate the spectral properties of
fluctuations in such systems. This provides a systematic derivation from first
principles of effective Langevin descriptions discussed in the literature. We
apply our approach to the totally asymmetric simple exclusion process, to
variants with an overall constraint on the total particle number and to a
two-species exclusion model. The theory provides semi-analytical results, these
are confirmed in numerical simulations, and give good approximations to
conventional exclusion models. These are recovered when the patch size is set
to unity.

View original: http://arxiv.org/abs/1112.0873