KPZ fixed point convergence of the ASEP and stochastic six-vertex models

Amol Aggarwal; Ivan Corwin; Milind Hegde

KPZ fixed point convergence of the ASEP and stochastic six-vertex models

Probability 2024-12-25 v1 Mathematical Physics math.MP

Authors: Amol Aggarwal , Ivan Corwin , Milind Hegde

Abstract

We consider the stochastic six-vertex (S6V) model and asymmetric simple exclusion process (ASEP) under general initial conditions which are bounded below lines of arbitrary slope at $\pm\infty$ . We show under Kardar-Parisi-Zhang (KPZ) scaling of time, space, and fluctuations that the height functions of these models converge to the KPZ fixed point. Previously, our results were known in the case of ASEP (for a particular direction in the rarefaction fan) via a comparison approach arXiv:2008.06584.

Keywords

KPZ fixed point ASEP stochastic six-vertex model height function scaling limit

Cite

@article{arxiv.2412.18117,
  title  = {KPZ fixed point convergence of the ASEP and stochastic six-vertex models},
  author = {Amol Aggarwal and Ivan Corwin and Milind Hegde},
  journal= {arXiv preprint arXiv:2412.18117},
  year   = {2024}
}

Comments

37 pages, 8 figures

KPZ fixed point convergence of the ASEP and stochastic six-vertex models

Abstract

Keywords

Cite

Comments

Related papers