Academy of Mathematics and Systems Science, CAS
Colloquia & Seminars

Speaker:	张灵夫博士, University of California Berkeley
Inviter:	骆顺龙研究员
Title:	Perturbation of TASEP: infinite order transition in the slow bond problem
Language:	Chinese
Time & Venue:	2023.06.26 10:30-11:30 数学院N613
Abstract:	Whether a localized microscopic defect will affect the macroscopic behavior of a system is a fundamental question in statistical mechanics. For the Totally Asymmetric Simple Exclusion Process (TASEP), a central model in the KPZ universality class, this problem is known as the ‘slow-bond problem’ and was originally posed by Janowsky and Lebowitz in the 90s: if the jump rate across one bond is decreased from 1 to 1-ε, is this effect detectable in the macroscopic current? Different groups of physicists, using a range of heuristics and numerical simulations, reached opposing conclusions. This problem was ultimately answered affirmatively in Basu-Sidoravicius-Sly for any positive ε. We then aim to more precisely understand the effect of the slow bond as ε tends to 0. We show that the slow-down effect in the macroscopic current, as a function of ε, is smaller than any polynomial. This explains why it was so challenging to predict on the basis of numerical simulations. Our proof focuses on the Last Passage Percolation formulation of TASEP, and uses geometric and probabilistic arguments (instead of exact formulas). This is based on joint work with Sourav Sarkar and Allan Sly.