Shock fluctuations in flat TASEP under critical scaling

Abstract

We consider TASEP with two types of particles starting at every second site. Particles to the left of the origin have jump rate $1$, while particles to the right have jump rate $\alpha$. When $\alpha <1$ there is a formation of a shock where the density jumps to $(1-\alpha )/2$. For $\alpha <1$ fixed, the statistics of the associated height functions around the shock is asymptotically (as time $t\to \infty$) a maximum of two independent random variables as shown in\cite{FN14}. In this paper we consider the critical scaling when $1-\alpha =a{t}^{-1/3}$, where $t\gg 1$ is the observation time. In that case the decoupling does not occur anymore. We determine the limiting distributions of the shock and numerically study its convergence as a function of $a$. We see that the convergence to $F_{\mathrm{GOE}}^2$ occurs quite rapidly as $a$ increases. The critical scaling is analogue to the one used in the last passage percolation to obtain the BBP transition processes\cite{BBP06}.

26 pages, 5 figures, LaTeX (minor improvements)

References in corpus (5)

• Fluctuation properties of the TASEP with periodic initial configuration
• Transition between Airy_1 and Airy_2 processes and TASEP fluctuations
• Airy kernel with two sets of parameters in directed percolation and random matrix theory
• Slow decorrelations in KPZ growth
• Last Branching in Directed Last Passage Percolation