The Annals of Applied Probability

Fluctuations of TASEP and LPP with general initial data

Ivan Corwin, Zhipeng Liu, and Dong Wang

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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 down-right 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.

Article information

Source
Ann. Appl. Probab., Volume 26, Number 4 (2016), 2030-2082.

Dates
Received: December 2014
Revised: June 2015
First available in Project Euclid: 1 September 2016

Permanent link to this document
https://projecteuclid.org/euclid.aoap/1472745451

Digital Object Identifier
doi:10.1214/15-AAP1139

Mathematical Reviews number (MathSciNet)
MR3543889

Zentralblatt MATH identifier
1356.82013

Subjects
Primary: C22 82B23: Exactly solvable models; Bethe ansatz 60H15: Stochastic partial differential equations [See also 35R60]

Keywords
TASEP last passage percolation Kardar–Parisi–Zhang

Citation

Corwin, Ivan; Liu, Zhipeng; Wang, Dong. Fluctuations of TASEP and LPP with general initial data. Ann. Appl. Probab. 26 (2016), no. 4, 2030--2082. doi:10.1214/15-AAP1139. https://projecteuclid.org/euclid.aoap/1472745451


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