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.
Cite
@article{arxiv.1709.05771,
title = {Variational formulas, Busemann functions, and fluctuation exponents for the corner growth model with exponential weights},
author = {Timo Seppäläinen},
journal= {arXiv preprint arXiv:1709.05771},
year = {2020}
}
Comments
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