Speaker: Sourav Sarkar
Date: November 20, 2025
Affiliation: TIFR, Mumbai

Abstract: Whether a localized microscopic defect will affect the macroscopic behaviour of a system is a fundamental question in statistical mechanics. For the totally asymmetric simple exclusion process (TASEP) on $\mathbb{Z}$, this problem was originally posed by Janowsky and Lebowitz and became famous as the ``slow-bond” problem. If the wait time of jump for a particle at the origin is increased from an exponential with rate $1$ to that with rate $1-\epsilon$, is this effect detectable in the macroscopic current? Different groups of physicists, using a range of heuristics and numerical simulations, reached opposing conclusions on whether the critical value of $\epsilon$ is $0$. This was ultimately resolved rigorously in Basu-Sidoravicius-Sly which established that $\epsilon_c=0$. In this talk, we will study the effect of the current as $\epsilon$ tends to $0$ and in doing so explain why it was so challenging to predict on the basis of numerical simulations. In particular, we show that the effect of the perturbation tends to 0 faster than any polynomial. This proves a conjecture by Costin-Lebowitz-Speer-Troiani. Our proof focuses on the last passage percolation formulation of TASEP. The talk is based on joint works with Allan Sly and Lingfu Zhang.