@article{70,
  abstract     = {We consider the totally asymmetric simple exclusion process in a critical scaling parametrized by a≥0, 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 lima→∞limT→∞ 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 airy processes.},
  author       = {Nejjar, Peter},
  issn         = {1980-0436},
  journal      = {Latin American Journal of Probability and Mathematical Statistics},
  number       = {2},
  pages        = {1311--1334},
  publisher    = {Instituto Nacional de Matematica Pura e Aplicada},
  title        = {{Transition to shocks in TASEP and decoupling of last passage times}},
  doi          = {10.30757/ALEA.v15-49},
  volume       = {15},
  year         = {2018},
}