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

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