Shock fluctuations in TASEP under a variety of time scalings

Abstract

We consider the totally asymmetric simple exclusion process (TASEP) with two different initial conditions with shock discontinuities, made by block of fully packed particles. Initially a second class particle is at the left of a shock discontinuity. Using multicolored TASEP we derive an exact formulas for the distribution of the second class particle and colored height functions. These are given in terms of the height function at different positions of a single TASEP configuration. We study the limiting distributions of second class particles (and colored height functions). The result depends on how the width blocks of particles scale with the observation time; we study a variety of such scalings.

The half-space Airy stat process

“…1 Such results hold around smooth limit shapes; hydrodynamical shocks can behave differently and we refer the reader to [33,40,[42][43][44][45]81] for some works on shocks. 2 The random initial condition on the two sides is recovered for most of the studied models using boundary sources, by the use of some Burke-type property [34,38], as shown for the exclusion process in [85].…”