Variational formulas, Busemann functions, and fluctuation exponents for the corner growth model with exponential weights

Abstract

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.

These notes were developed for the AMS Short Course on Random Growth Models (January 2017) and for the Research School on Random Structures in Statistical Mechanics and Mathematical Physics at CIRM in Marseille Luminy (March 2017). Later versions added two sections and made edits and corrections

References in corpus (3)

• Limiting shape for directed percolation models
• Variational formulas and disorder regimes of random walks in random potentials
• Random coalescing geodesics in first-passage percolation

Cited by in corpus (4)

• Right-tail moderate deviations in the exponential last-passage percolation
• Optimal-order exit point bounds in exponential last-passage percolation via the coupling technique
• Coalescence estimates for the corner growth model with exponential weights
• Quenched Central Limit Theorem in a Corner Growth Setting