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Variational formulas, Busemann functions, and fluctuation exponents for the corner growth model with exponential weights
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These lecture notes discuss several related features of the exactly solvable two-dimensional corner growth model with exponentially distributed weights. A key property of this model is the availability of a fairly explicit stationary version that possesses useful independence properties. With the help of couplings and estimates, we prove the existence of Busemann functions for this model, and the precise values of the longitudinal and transversal fluctuation exponents for the stationary corner growth model. The Busemann functions in turn furnish extremals for variational formulas that describe limiting shape functions.
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Permutation invariance in last-passage percolation and the distribution of the Busemann process
The joint law of Busemann increments in i.i.d. exponential LPP is exactly represented by last-passage increments on a finite grid with inhomogeneous exponential weights.
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