Joint distribution of Busemann functions in the exactly solvable corner growth model

Abstract

The 1+1 dimensional corner growth model with exponential weights is a centrally important exactly solvable model in the Kardar-Parisi-Zhang class of statistical mechanical models. While significant progress has been made on the fluctuations of the growing random shape, understanding of the optimal paths, or geodesics, is less developed. The Busemann function is a useful analytical tool for studying geodesics. This paper describes the joint distribution of the Busemann functions, simultaneously in all directions of growth. As applications of this description we derive a marked point process representation for the Busemann function across a single lattice edge and calculate some marginal distributions of Busemann functions and semi-infinite geodesics.

arXiv commentImproved exposition with figures

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Cited by in corpus (10)

• Non-existence of bi-infinite geodesics in the exponential corner growth model
• Busemann functions and Gibbs measures in directed polymer models on ${\mathbb{Z}}^2$
• The stationary horizon and semi-infinite geodesics in the directed landscape
• Modified Macdonald polynomials and the multispecies zero range process: II
• Jointly invariant measures for the Kardar-Parisi-Zhang Equation
• Intertwining the Busemann process of the directed polymer model
• Poisson limit theorems for the Robinson-Schensted correspondence and for the multi-line Hammersley process
• Jointly stationary solutions of periodic Burgers flow
• Second Class Particle Behaviour in Blocking ASEP
• Simultaneous global inviscid Burgers flows with periodic Poisson forcing