Right-tail moderate deviations in the exponential last-passage percolation

Abstract

We study moderate deviations in the exponential corner growth model, both in the bulk setting and the increment-stationary setting. The main results are sharp right-tail bounds on the last-passage time and the exit point of the increment-stationary process. The arguments utilize calculations with the stationary version and a moment generating function identity due to E. Rains, for which we give a short probabilistic proof. As applications of the deviation bounds, we derive upper bounds on the speed of distributional convergence in the Busemann function and competition interface limits.

40 pages, 6 figures

References in corpus (4)

• Large deviations for some corner growth models with inhomogeneity
• A mean identity for longest increasing subsequence problems
• Variational formulas, Busemann functions, and fluctuation exponents for the corner growth model with exponential weights
• Coalescence estimates for the corner growth model with exponential weights

Cited by in corpus (3)

• The stationary horizon and semi-infinite geodesics in the directed landscape
• Optimal-order exit point bounds in exponential last-passage percolation via the coupling technique
• Coalescence estimates for the corner growth model with exponential weights