# Transition to Shocks in TASEP and Decoupling of Last Passage Times

## TL;DR

This paper studies the behavior of the TASEP model near shocks, revealing how last passage times decouple and how the process transitions from correlated to independent regimes, with implications for related percolation models.

## Contribution

It provides new bounds on the limiting laws of TASEP at shocks and demonstrates the decoupling of last passage times, extending results to general last-passage percolation models.

## Key findings

- Limits recover product law at large shocks.
- Bounds on two-point functions of Airy processes.
- Application to general last-passage percolation models.

## Abstract

We consider the totally asymmetric simple exclusion process in a critical scaling parametrized by $a\geq0$, which creates a shock in the particle density of order $aT^{-1/3},$ $T$ the observation time. When starting from step initial data, we provide bounds on the limiting law which in particular imply that in the double limit $\lim_{a \to \infty}\lim_{T \to \infty}$ one recovers the product limit law and the degeneration of the correlation length observed at shocks of order $1$. This result is shown to apply to a general last-passage percolation model. We also obtain bounds on the two-point functions of several $\mathrm{Airy}$ processes.