Moderate deviation and exit time estimates for stationary Last Passage Percolation

Abstract

We consider planar stationary exponential Last Passage Percolation in the positive quadrant with boundary weights. For $\rho \in (0,1)$ and points $v_N=((1-\rho {)}^{2}N,{\rho }^{2}N)$ going to infinity along the characteristic direction, we establish right tail estimates with the optimal exponent for the exit time of the geodesic, along with optimal exponent estimates for the upper tail moderate deviations for the passage time. For the case $\rho =\frac{1}{2}$ in the stationary model, we establish the lower bound estimate with the optimal exponent for the lower tail of the passage time. Our arguments are based on moderate deviation estimates for point-to-point and point-to-line exponential Last Passage Percolation which are obtained via random matrix estimates.

arXiv comment15 pages

References in corpus (7)

• Shape Fluctuations and Random Matrices
• Discrete polynuclear growth and determinantal processes
• Fluctuation properties of the TASEP with periodic initial configuration
• Airy kernel with two sets of parameters in directed percolation and random matrix theory
• Limit process of stationary TASEP near the characteristic line
• Time-time covariance for last passage percolation with generic initial profile
• Non-existence of bi-infinite geodesics in the exponential corner growth model

Cited by in corpus (4)

• 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
• Mixing times and cutoff for the TASEP in the high and low density phase
• Coupling derivation of optimal-order central moment bounds in exponential last-passage percolation