Generalized Green Functions and current correlations in the TASEP
arXiv:1007.1391 · doi:10.1007/s10955-011-0133-y
Abstract
We study correlation functions of the totally asymmetric simple exclusion process (TASEP) in discrete time with backward sequential update. We prove a determinantal formula for the generalized Green function which describes transitions between positions of particles at different individual time moments. In particular, the generalized Green function defines a probability measure at staircase lines on the space-time plane. The marginals of this measure are the TASEP correlation functions in the space-time region not covered by the standard Green function approach. As an example, we calculate the current correlation function that is the joint probability distribution of times taken by selected particles to travel given distance. An asymptotic analysis shows that current fluctuations converge to the process.
46 pages, 3 figures
References in corpus (9)
- Fluctuation properties of the TASEP with periodic initial configuration
- Transition between Airy_1 and Airy_2 processes and TASEP fluctuations
- Current Distribution and random matrix ensembles for an integrable asymmetric fragmentation process
- Airy kernel with two sets of parameters in directed percolation and random matrix theory
- Large time asymptotics of growth models on space-like paths II: PNG and parallel TASEP
- Dynamics of a tagged particle in the asymmetric exclusion process with the step initial condition
- Slow decorrelations in KPZ growth
- Determinant solution for the Totally Asymmetric Exclusion Process with parallel update
- Determinant solution for the Totally Asymmetric Exclusion Process with parallel update II. Ring geometry