Limit process of stationary TASEP near the characteristic line

TL;DR

This paper investigates the multi-point distribution of current fluctuations in stationary TASEP near the characteristic line, revealing new fluctuation regimes and connecting to last percolation models and tandem queues.

Contribution

It extends the understanding of TASEP fluctuations by analyzing behavior away from the characteristic line and establishing links to last percolation and queueing models.

Findings

Determined multi-point distribution of current fluctuations away from the characteristic line.

Identified a t^{2/3} fluctuation regime distinct from the t^{1/3} regime on the characteristic line.

Connected TASEP fluctuations to directed last percolation and tandem queue processes.

Abstract

The totally asymmetric simple exclusion process (TASEP) on Z with the Bernoulli-rho measure as initial conditions, 0<rho<1, is stationary. It is known that along the characteristic line, the current fluctuates as of order t^{1/3}. The limiting distribution has also been obtained explicitly. In this paper we determine the limiting multi-point distribution of the current fluctuations moving away from the characteristics by the order t^{2/3}. The main tool is the analysis of a related directed last percolation model. We also discuss the process limit in tandem queues in equilibrium.