Fluctuations of TASEP and LPP with general initial data

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.

44 pages, 6 figures

References in corpus (4)

• Fluctuations of the one-dimensional polynuclear growth model with external sources
• A determinantal formula for the GOE Tracy-Widom distribution
• Airy processes and variational problems
• Slow decorrelations in KPZ growth

Cited by in corpus (2)

• Reflected Brownian motions in the KPZ universality class
• Limit shape and fluctuations for exactly solvable inhomogeneous corner growth models