Physics – Mathematical Physics
Scientific paper
2010-02-18
J. Stat. Physics, 140, 2010, p. 232-267
Physics
Mathematical Physics
46 pages, 3 figures, LaTeX; Extended explanations in the first two sections
Scientific paper
We consider the totally asymmetric simple exclusion process (TASEP) with two-sided Bernoulli initial condition, i.e., with left density rho_- and right density rho_+. We consider the associated height function, whose discrete gradient is given by the particle occurrences. Macroscopically one has a deterministic limit shape with a shock or a rarefaction fan depending on the values of rho_{+/-}. We characterize the large time scaling limit of the fluctuations as a function of the densities rho_{+/-} and of the different macroscopic regions. Moreover, using a slow decorrelation phenomena, the results are extended from fixed time to the whole space-time, except along the some directions (the characteristic solutions of the related Burgers equation) where the problem is still open. On the way to proving the results for TASEP, we obtain the limit processes for the fluctuations in a class of corner growth processes with external sources, of equivalently for the last passage time in a directed percolation model with two-sided boundary conditions. Additionally, we provide analogous results for eigenvalues of perturbed complex Wishart (sample covariance) matrices.
Corwin Ivan
Ferrari Patrik L.
Peche Sandrine
No associations
LandOfFree
Limit processes for TASEP with shocks and rarefaction fans does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.
If you have personal experience with Limit processes for TASEP with shocks and rarefaction fans, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Limit processes for TASEP with shocks and rarefaction fans will most certainly appreciate the feedback.
Profile ID: LFWR-SCP-O-405555