We provide the first tight bounds on the lower tail probability of the one-point distribution of
the Kardar–Parisi–Zhang (KPZ) equation with narrow wedge initial data. Our bounds hold …

In this paper, we study lower tail probabilities of the height function $\mathfrak {h}(M, N) $ of
the stochastic six-vertex model. We introduce a novel combinatorial approach to …

We consider the large deviations from the hydrodynamic limit of the Totally Asymmetric
Simple Exclusion Process (TASEP). This problem was studied by Jensen and Varadhan and …

Abstract We consider the Kardar-Parisi-Zhang (KPZ) equation for the stochastic growth of an
interface of height $ h (x, t) $ on the positive half line with boundary condition $\partial_x h (x …

We consider the variational problem associated with the Freidlin–Wentzell Large Deviation
Principle (LDP) for the Stochastic Heat Equation (SHE). For a general class of initial-terminal …

This article studies several properties of the half-space last passage percolation, in
particular the two-time covariance. We show that, when the two end-points are at small …

We analyze the high moments of the Stochastic Heat Equation (SHE) via a transformation to
the attractive Brownian Particles (BPs), which are Brownian motions interacting via pairwise …

We prove the upper-tail Large Deviation Principle (LDP) for the parabolic Airy process and
characterize the limit shape of the directed landscape under the upper-tail conditioning. The …

We consider the half-line stochastic heat equation (SHE) with Robin boundary parameter A=-
1 2 A=-1 2. Under narrow wedge initial condition, we compute every positive (including non …

The Airy point process is a determinantal point process that arises from the spectral edge of
the Gaussian Unitary Ensemble. In this paper, we establish a large deviation principle for the …