Related papers: Conditional exponential directed last passage perc…
We survey some results and applications of last percolation models of which the limiting distribution can be evaluated.
Directed last passage percolation models on the plane, where one studies the weight as well as the geometry of optimizing paths (called polymers) in a field of i.i.d. weights, are paradigm examples of models in the KPZ universality class.…
For exponential last passage percolation on the plane we analyse the probability that the point-to-line geodesic exhibits an atypically large transversal fluctuation at the endpoint as well as the probability that the point-to-point…
We consider the totally asymmetric simple exclusion process with initial conditions and/or jump rates such that shocks are generated. If the initial condition is deterministic, then the shock at time t will have a width of order t^{1/3}. We…
This short note provides a large-deviation-based upper bound on the growth rate of directed last passage percolation (LPP) using the entropy of the normalized direction vector.
We introduce and study a model of directed last-passage percolation in planar layered environment. This environment is represented by an array of random exponential clocks arranged in blocks, for each block the average waiting times depend…
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…
This note establishes a universal directed landscape limit for last passage percolation models in an intermediate scaling regime. We find as a quick consequence the transversal fluctuations for geodesics taken near the axis. We extend the…
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 macroscopic distance, then the first order correction to the…
In directed last passage site percolation with i.i.d.~random weights with finite support over a $n\times\lfloor n^{\alpha}\rfloor$ grid, we prove that for $n$ large enough, the order of the $r$-th central moment, $1\le r<+\infty$, of the…
We consider directed last-passage percolation on the random graph G = (V,E) where V = Z and each edge (i,j), for i < j, is present in E independently with some probability 0 < p <= 1. To every present edge (i,j) we attach i.i.d. random…
The aim of this paper is to study the law of the last passage time of a linear diffusion to a curved boundary. We start by giving a general expression for the density of such a random variable under some regularity assumptions. Following…
This is the second, and last paper in which we address the behavior of oriented first passage percolation on the hypercube in the limit of large dimensions. We prove here that the extremal process converges to a Cox process with exponential…
The focus of this article is on the different behavior of large deviations of random subadditive functionals above the mean versus large deviations below the mean in two random media models. We consider the point-to-point first passage…
In a growing number of strongly disordered and dense systems, the dynamics of a particle pulled by an external force field exhibits super-diffusion. In the context of glass forming systems, super cooled glasses and contamination spreading…
In this paper we consider an equilibrium last-passage percolation model on an environment given by a compound two-dimensional Poisson process. We prove an $\LL^2$-formula relating the initial measure with the last-passage percolation time.…
We consider time correlation for KPZ growth in 1+1 dimensions in a neighborhood of a characteristics. We prove convergence of the covariance with droplet, flat and stationary initial profile. In particular, this provides a rigorous proof of…
We study last passage percolation in a half-quadrant, which we analyze within the framework of Pfaffian Schur processes. For the model with exponential weights, we prove that the fluctuations of the last passage time to a point on the…
We consider the half-space geometric Last Passage Percolation model starting with stationary measures. We obtain exact formulas for LPP value along the diagonal $(N,N)$ across the entire phase diagram. We also obtain the limits of these…
The study of transversal fluctuations of the optimal path is a crucial aspect of the Kardar-Parisi-Zhang (KPZ) universality class. In this work, we establish the large deviation limit for the midpoint transversal fluctuations in a general…