Fluctuations of TASEP and LPP with general initial data

TL;DR

This paper establishes variational formulas for the distribution of TASEP and last passage percolation with general initial data, advancing understanding of the KPZ universality class's fixed point.

Contribution

It provides new variational formulas for TASEP and LPP with general initial conditions, extending previous results and supporting KPZ universality conjectures.

Findings

Derived Airy process variational formulas for TASEP with general initial data

Extended variational formulas to inhomogeneous last passage percolation models

Contributed to the theoretical understanding of KPZ fixed point

Abstract

We prove Airy process variational formulas for the one-point probability distribution of (discrete time parallel update) TASEP with general initial data, as well as last passage percolation from a general lattice path to a point. We also consider variants of last passage percolation with inhomogeneous parameter geometric weights and provide variational formulas of a similar nature. This proves one aspect of the conjectural description of the renormalization fixed point of the Kardar-Parisi-Zhang universality class.