A Large deviation principle for last passage times in an asymmetric Bernoulli potential

Abstract

We prove a large deviation principle and give an expression for the rate function, for the last passage time in a Bernoulli environment. The model is exactly solvable and its invariant version satisfies a Burke-type property. Finally, we compute explicit limiting logarithmic moment generating functions for both the classical and the invariant models. The shape function of this model exhibits a flat edge in certain directions, and we also discuss the rate function and limiting log-moment generating functions in those directions.

Fractional moments of the Stochastic Heat Equation

“…The upper tail problem has also been studied for several other models in the class of integrable systems starting from the fluctuation results and LDP for the longest increasing subsequence [Kim96, Sep98, DZ99, BDJ99]. There are also analogous results on upper-tail LDP for integrable polymer models [GS13,Jan15], and also for last passage percolation in Bernoulli and white noise environments [CG18a,Jan19] and inhomogeneous corner growth models [EJ15].…”