The
-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. We describe 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.