# Zone clearance in an infinite TASEP with a step initial condition

## TL;DR

This paper investigates the probability of a specific zone in an infinite TASEP becoming empty over time, providing exact results for some observables and simulation-based insights for others, relevant to biological and traffic models.

## Contribution

It introduces new observables related to zone clearance in TASEP, deriving exact formulas and employing simulations for complex history-dependent quantities.

## Key findings

- Exact expressions for single-time clearance probabilities
- Monte Carlo simulations for history-dependent observables
- Partial phenomenological predictions for complex quantities

## Abstract

The TASEP is a paradigmatic model of out-of-equilibrium statistical physics, for which many quantities have been computed, either exactly or by approximate methods. In this work we study two new kinds of observables that have some relevance in biological or traffic models. They represent the probability for a given clearance zone of the lattice to be empty (for the first time) at a given time, starting from a step density profile. Exact expressions are obtained for single-time quantities, while more involved history-dependent observables are studied by Monte Carlo simulation, and partially predicted by a phenomenological approach.